自然对数表,以2为底的对数表,常用对数表三表合一

自然对数表,以2为底的对数表,常用对数表三表合一
自然对数表,以2为底的对数表,常用对数表三表合一

Natural Logarithms Table - ln N

N0123456789 1.003z99503.019803.029559.039221.048790.058269.067659.076961.086178 1.1.095310.104360.113329.122218.131028.139762.148420.157004.165514.173953 1.2.182322.190620.198851.207014.215111.223144.231112.239017.246860.254642 1.3.262364.270027.277632.285179.292670.300105.307485.314811.322083.329304 1.4.336472.343590.350657.357674.364643.371564.378436.385262.392042.398776 1.5.405465.412110.418710.425268.431782.438255.444686.451076.457425.463734 1.6.470004.476234.482426.488580.494696.500775.506818.512824.518794.524729 1.7.530628.536493.542324.548121.553885.559616.565314.570980.576613.582216 1.8.587787.593327.598837.604316.609766.615186.620576.625938.631272.636577 1.9.641854.647103.652325.657520.662688.667829.672944.678034.683097.688135 N0123456789 2.0.693147.698135.703098.708036.712950.717840.722706.727549.732368.737164 2.1.741937.746688.751416.756122.760806.765468.770108.774727.779325.783902 2.2.788457.792993.797507.802002.806476.810930.815365.819780.824175.828552 2.3.832909.837248.841567.845868.850151.854415.858662.862890.867100.871293 2.4.875469.879627.883768.887891.891998.896088.900161.904218.908259.912283 2.5.916291.920283.924259.928219.932164.936093.940007.943906.947789.951658 2.6.955511.959350.963174.966984.970779.974560.978326.982078.985817.989541 2.7.993252.996949 1.00063 1.00430 1.00796 1.01160 1.01523 1.01885 1.02245 1.02604 2.8 1.02962 1.03318 1.03674 1.04028 1.04380 1.04732 1.05082 1.05431 1.05779 1.06126 2.9 1.06471 1.06815 1.07158 1.07500 1.07841 1.08181 1.08519 1.08856 1.09192 1.09527 N0123456789 3.0 1.09861 1.10194 1.10526 1.10856 1.11186 1.11514 1.11841 1.12168 1.12493 1.12817 3.1 1.13140 1.13462 1.13783 1.14103 1.14422 1.14740 1.15057 1.15373 1.15688 1.16002 3.2 1.16315 1.16627 1.16938 1.17248 1.17557 1.17865 1.18173 1.18479 1.18784 1.19089 3.3 1.19392 1.19695 1.19996 1.20297 1.20597 1.20896 1.21194 1.21491 1.21788 1.22083 3.4 1.22378 1.22671 1.22964 1.23256 1.23547 1.23837 1.24127 1.24415 1.24703 1.24990 3.5 1.25276 1.25562 1.25846 1.26130 1.26413 1.26695 1.26976 1.27257 1.27536 1.27815 3.6 1.28093 1.28371 1.28647 1.28923 1.29198 1.29473 1.29746 1.30019 1.30291 1.30563 3.7 1.30833 1.31103 1.31372 1.31641 1.31909 1.32176 1.32442 1.32708 1.32972 1.33237 3.8 1.33500 1.33763 1.34025 1.34286 1.34547 1.34807 1.35067 1.35325 1.35584 1.35841 3.9 1.36098 1.36354 1.36609 1.36864 1.37118 1.37372 1.37624 1.37877 1.38128 1.38379 N0123456789 4.0 1.38629 1.38879 1.39128 1.39377 1.39624 1.39872 1.40118 1.40364 1.40610 1.40854 4.1 1.41099 1.41342 1.41585 1.41828 1.42070 1.42311 1.42552 1.42792 1.43031 1.43270 4.2 1.43508 1.43746 1.43984 1.44220 1.44456 1.44692 1.44927 1.45161 1.45395 1.45629 4.3 1.45862 1.46094 1.46326 1.46557 1.46787 1.47018 1.47247 1.47476 1.47705 1.47933 4.4 1.48160 1.48387 1.48614 1.48840 1.49065 1.49290 1.49515 1.49739 1.49962 1.50185 4.5 1.50408 1.50630 1.50851 1.51072 1.51293 1.51513 1.51732 1.51951 1.52170 1.52388 4.6 1.52606 1.52823 1.53039 1.53256 1.53471 1.53687 1.53902 1.54116 1.54330 1.54543 4.7 1.54756 1.54969 1.55181 1.55393 1.55604 1.55814 1.56025 1.56235 1.56444 1.56653 4.8 1.56862 1.57070 1.57277 1.57485 1.57691 1.57898 1.58104 1.58309 1.58515 1.58719 4.9 1.58924 1.59127 1.59331 1.59534 1.59737 1.59939 1.60141 1.60342 1.60543 1.60744 N0123456789 5.0 1.60944 1.61144 1.61343 1.61542 1.61741 1.61939 1.62137 1.62334 1.62531 1.62728 5.1 1.62924 1.63120 1.63315 1.63511 1.63705 1.63900 1.64094 1.64287 1.64481 1.64673 5.2 1.64866 1.65058 1.65250 1.65441 1.65632 1.65823 1.66013 1.66203 1.66393 1.66582 5.3 1.66771 1.66959 1.67147 1.67335 1.67523 1.67710 1.67896 1.68083 1.68269 1.68455 5.4 1.68640 1.68825 1.69010 1.69194 1.69378 1.69562 1.69745 1.69928 1.70111 1.70293 5.5 1.70475 1.70656 1.70838 1.71019 1.71199 1.71380 1.71560 1.71740 1.71919 1.72098 5.6 1.72277 1.72455 1.72633 1.72811 1.72988 1.73166 1.73342 1.73519 1.73695 1.73871 5.7 1.74047 1.74222 1.74397 1.74572 1.74746 1.74920 1.75094 1.75267 1.75440 1.75613 5.8 1.75786 1.75958 1.76130 1.76302 1.76473 1.76644 1.76815 1.76985 1.77156 1.77326 5.9 1.77495 1.77665 1.77834 1.78002 1.78171 1.78339 1.78507 1.78675 1.78842 1.79009 N0123456789 6.0 1.79176 1.79342 1.79509 1.79675 1.79840 1.80006 1.80171 1.80336 1.80500 1.80665 6.1 1.80829 1.80993 1.81156 1.81319 1.81482 1.81645 1.81808 1.81970 1.82132 1.82294 6.2 1.82455 1.82616 1.82777 1.82938 1.83098 1.83258 1.83418 1.83578 1.83737 1.83896 6.3 1.84055 1.84214 1.84372 1.84530 1.84688 1.84845 1.85003 1.85160 1.85317 1.85473 6.4 1.85630 1.85786 1.85942 1.86097 1.86253 1.86408 1.86563 1.86718 1.86872 1.87026 6.5 1.87180 1.87334 1.87487 1.87641 1.87794 1.87947 1.88099 1.88251 1.88403 1.88555 6.6 1.88707 1.88858 1.89010 1.89160 1.89311 1.89462 1.89612 1.89762 1.89912 1.90061 6.7 1.90211 1.90360 1.90509 1.90658 1.90806 1.90954 1.91102 1.91250 1.91398 1.91545 6.8 1.91692 1.91839 1.91986 1.92132 1.92279 1.92425 1.92571 1.92716 1.92862 1.93007 6.9 1.93152 1.93297 1.93442 1.93586 1.93730 1.93874 1.94018 1.94162 1.94305 1.94448 N0123456789 7.0 1.94591 1.94734 1.94876 1.95019 1.95161 1.95303 1.95445 1.95586 1.95727 1.95869 7.1 1.96009 1.96150 1.96291 1.96431 1.96571 1.96711 1.96851 1.96991 1.97130 1.97269 7.2 1.97408 1.97547 1.97685 1.97824 1.97962 1.98100 1.98238 1.98376 1.98513 1.98650 7.3 1.98787 1.98924 1.99061 1.99198 1.99334 1.99470 1.99606 1.99742 1.99877 2.00013 7.4 2.00148 2.00283 2.00418 2.00553 2.00687 2.00821 2.00956 2.01089 2.01223 2.01357 7.5 2.01490 2.01624 2.01757 2.01890 2.02022 2.02155 2.02287 2.02419 2.02551 2.02683 7.6 2.02815 2.02946 2.03078 2.03209 2.03340 2.03471 2.03601 2.03732 2.03862 2.03992 7.7 2.04122 2.04252 2.04381 2.04511 2.04640 2.04769 2.04898 2.05027 2.05156 2.05284 7.8 2.05412 2.05540 2.05668 2.05796 2.05924 2.06051 2.06179 2.06306 2.06433 2.06560 7.9 2.06686 2.06813 2.06939 2.07065 2.07191 2.07317 2.07443 2.07568 2.07694 2.07819 N0123456789 8.0 2.07944 2.08069 2.08194 2.08318 2.08443 2.08567 2.08691 2.08815 2.08939 2.09063 8.1 2.09186 2.09310 2.09433 2.09556 2.09679 2.09802 2.09924 2.10047 2.10169 2.10291 8.2 2.10413 2.10535 2.10657 2.10779 2.10900 2.11021 2.11142 2.11263 2.11384 2.11505 8.3 2.11626 2.11746 2.11866 2.11986 2.12106 2.12226 2.12346 2.12465 2.12585 2.12704 8.4 2.12823 2.12942 2.13061 2.13180 2.13298 2.13417 2.13535 2.13653 2.13771 2.13889 8.5 2.14007 2.14124 2.14242 2.14359 2.14476 2.14593 2.14710 2.14827 2.14943 2.15060 8.6 2.15176 2.15292 2.15409 2.15524 2.15640 2.15756 2.15871 2.15987 2.16102 2.16217 8.7 2.16332 2.16447 2.16562 2.16677 2.16791 2.16905 2.17020 2.17134 2.17248 2.17361 8.8 2.17475 2.17589 2.17702 2.17816 2.17929 2.18042 2.18155 2.18267 2.18380 2.18493 8.9 2.18605 2.18717 2.18830 2.18942 2.19054 2.19165 2.19277 2.19389 2.19500 2.19611 N0123456789 9.0 2.19722 2.19834 2.19944 2.20055 2.20166 2.20276 2.20387 2.20497 2.20607 2.20717 9.1 2.20827 2.20937 2.21047 2.21157 2.21266 2.21375 2.21485 2.21594 2.21703 2.21812 9.2 2.21920 2.22029 2.22138 2.22246 2.22354 2.22462 2.22570 2.22678 2.22786 2.22894 9.3 2.23001 2.23109 2.23216 2.23324 2.23431 2.23538 2.23645 2.23751 2.23858 2.23965 9.4 2.24071 2.24177 2.24284 2.24390 2.24496 2.24601 2.24707 2.24813 2.24918 2.25024 9.5 2.25129 2.25234 2.25339 2.25444 2.25549 2.25654 2.25759 2.25863 2.25968 2.26072 9.6 2.26176 2.26280 2.26384 2.26488 2.26592 2.26696 2.26799 2.26903 2.27006 2.27109 9.7 2.27213 2.27316 2.27419 2.27521 2.27624 2.27727 2.27829 2.27932 2.28034 2.28136 9.8 2.28238 2.28340 2.28442 2.28544 2.28646 2.28747 2.28849 2.28950 2.29051 2.29152

9.9 2.29253 2.29354 2.29455 2.29556 2.29657 2.29757 2.29858 2.29958 2.30058 2.30158

10.02.30259 2.30358 2.30458 2.30558 2.30658 2.30757 2.30857 2.30956 2.31055 2.31154

Base-2 Logarithms Table - log

2

N

N0123456789 1.00.014355.028569.042644.056584.070389.084064.097611.111031.124328 1.1.137504.150560.163499.176323.189034.201634.214125.226509.238787.250962 1.2.263034.275007.286881.298658.310340.321928.333424.344828.356144.367371 1.3.378512.389567.400538.411426.422233.432959.443607.454176.464668.475085 1.4.485427.495695.505891.516015.526069.536053.545968.555816.565597.575312 1.5.584963.594549.604071.613532.622930.632268.641546.650765.659925.669027 1.6.678072.687061.695994.704872.713696.722466.731183.739848.748461.757023 1.7.765535.773996.782409.790772.799087.807355.815575.823749.831877.839960 1.8.847997.855990.863938.871844.879706.887525.895303.903038.910733.918386 1.9.925999.933573.941106.948601.956057.963474.970854.978196.985500.992768 N0123456789 2.0 1.00000 1.00720 1.01436 1.02148 1.02857 1.03562 1.04264 1.04963 1.05658 1.06350 2.1 1.07039 1.07724 1.08406 1.09085 1.09761 1.10434 1.11103 1.11770 1.12433 1.13093 2.2 1.13750 1.14405 1.15056 1.15704 1.16350 1.16993 1.17632 1.18269 1.18903 1.19535 2.3 1.20163 1.20789 1.21412 1.22033 1.22651 1.23266 1.23879 1.24489 1.25096 1.25701 2.4 1.26303 1.26903 1.27501 1.28096 1.28688 1.29278 1.29866 1.30451 1.31034 1.31615 2.5 1.32193 1.32769 1.33342 1.33914 1.34483 1.35050 1.35614 1.36177 1.36737 1.37295 2.6 1.37851 1.38405 1.38957 1.39506 1.40054 1.40599 1.41143 1.41684 1.42223 1.42761 2.7 1.43296 1.43829 1.44361 1.44890 1.45418 1.45943 1.46467 1.46989 1.47508 1.48027 2.8 1.48543 1.49057 1.49570 1.50080 1.50589 1.51096 1.51602 1.52105 1.52607 1.53107 2.9 1.53605 1.54102 1.54597 1.55090 1.55582 1.56071 1.56560 1.57046 1.57531 1.58015 N0123456789 3.0 1.58496 1.58976 1.59455 1.59932 1.60407 1.60881 1.61353 1.61824 1.62293 1.62761 3.1 1.63227 1.63691 1.64155 1.64616 1.65076 1.65535 1.65992 1.66448 1.66903 1.67356 3.2 1.67807 1.68257 1.68706 1.69153 1.69599 1.70044 1.70487 1.70929 1.71370 1.71809 3.3 1.72247 1.72683 1.73118 1.73552 1.73985 1.74416 1.74846 1.75275 1.75702 1.76129 3.4 1.76553 1.76977 1.77400 1.77821 1.78241 1.78660 1.79077 1.79494 1.79909 1.80323 3.5 1.80735 1.81147 1.81558 1.81967 1.82375 1.82782 1.83188 1.83592 1.83996 1.84398 3.6 1.84800 1.85200 1.85599 1.85997 1.86394 1.86790 1.87184 1.87578 1.87971 1.88362 3.7 1.88753 1.89142 1.89530 1.89918 1.90304 1.90689 1.91073 1.91456 1.91839 1.92220 3.8 1.92600 1.92979 1.93357 1.93734 1.94111 1.94486 1.94860 1.95233 1.95606 1.95977 3.9 1.96347 1.96717 1.97085 1.97453 1.97820 1.98185 1.98550 1.98914 1.99277 1.99639 N0123456789 4.0 2.00000 2.00360 2.00720 2.01078 2.01436 2.01792 2.02148 2.02503 2.02857 2.03210 4.1 2.03562 2.03914 2.04264 2.04614 2.04963 2.05311 2.05658 2.06005 2.06350 2.06695 4.2 2.07039 2.07382 2.07724 2.08066 2.08406 2.08746 2.09085 2.09424 2.09761 2.10098 4.3 2.10434 2.10769 2.11103 2.11437 2.11770 2.12102 2.12433 2.12763 2.13093 2.13422 4.4 2.13750 2.14078 2.14405 2.14731 2.15056 2.15381 2.15704 2.16027 2.16350 2.16672 4.5 2.16993 2.17313 2.17632 2.17951 2.18269 2.18587 2.18903 2.19219 2.19535 2.19849 4.6 2.20163 2.20477 2.20789 2.21101 2.21412 2.21723 2.22033 2.22342 2.22651 2.22959 4.7 2.23266 2.23573 2.23879 2.24184 2.24489 2.24793 2.25096 2.25399 2.25701 2.26003 4.8 2.26303 2.26604 2.26903 2.27202 2.27501 2.27798 2.28096 2.28392 2.28688 2.28983 4.9 2.29278 2.29572 2.29866 2.30159 2.30451 2.30743 2.31034 2.31325 2.31615 2.31904 N0123456789 5.0 2.32193 2.32481 2.32769 2.33056 2.33342 2.33628 2.33914 2.34199 2.34483 2.34767 5.1 2.35050 2.35332 2.35614 2.35896 2.36177 2.36457 2.36737 2.37016 2.37295 2.37573 5.2 2.37851 2.38128 2.38405 2.38681 2.38957 2.39232 2.39506 2.39780 2.40054 2.40327 5.3 2.40599 2.40871 2.41143 2.41414 2.41684 2.41954 2.42223 2.42492 2.42761 2.43029 5.4 2.43296 2.43563 2.43829 2.44095 2.44361 2.44626 2.44890 2.45154 2.45418 2.45681 5.5 2.45943 2.46205 2.46467 2.46728 2.46989 2.47249 2.47508 2.47768 2.48027 2.48285 5.6 2.48543 2.48800 2.49057 2.49313 2.49570 2.49825 2.50080 2.50335 2.50589 2.50843 5.7 2.51096 2.51349 2.51602 2.51854 2.52105 2.52356 2.52607 2.52857 2.53107 2.53356 5.8 2.53605 2.53854 2.54102 2.54350 2.54597 2.54844 2.55090 2.55336 2.55582 2.55827 5.9 2.56071 2.56316 2.56560 2.56803 2.57046 2.57289 2.57531 2.57773 2.58015 2.58256 N0123456789 6.0 2.58496 2.58736 2.58976 2.59216 2.59455 2.59694 2.59932 2.60170 2.60407 2.60644 6.1 2.60881 2.61117 2.61353 2.61589 2.61824 2.62059 2.62293 2.62527 2.62761 2.62994 6.2 2.63227 2.63459 2.63691 2.63923 2.64155 2.64386 2.64616 2.64847 2.65076 2.65306 6.3 2.65535 2.65764 2.65992 2.66221 2.66448 2.66676 2.66903 2.67129 2.67356 2.67582 6.4 2.67807 2.68032 2.68257 2.68482 2.68706 2.68930 2.69153 2.69377 2.69599 2.69822 6.5 2.70044 2.70266 2.70487 2.70708 2.70929 2.71149 2.71370 2.71589 2.71809 2.72028 6.6 2.72247 2.72465 2.72683 2.72901 2.73118 2.73335 2.73552 2.73769 2.73985 2.74201 6.7 2.74416 2.74631 2.74846 2.75061 2.75275 2.75489 2.75702 2.75916 2.76129 2.76341 6.8 2.76553 2.76765 2.76977 2.77189 2.77400 2.77610 2.77821 2.78031 2.78241 2.78450 6.9 2.78660 2.78869 2.79077 2.79286 2.79494 2.79701 2.79909 2.80116 2.80323 2.80529 N0123456789 7.0 2.80735 2.80941 2.81147 2.81352 2.81558 2.81762 2.81967 2.82171 2.82375 2.82579 7.1 2.82782 2.82985 2.83188 2.83390 2.83592 2.83794 2.83996 2.84197 2.84398 2.84599 7.2 2.84800 2.85000 2.85200 2.85400 2.85599 2.85798 2.85997 2.86196 2.86394 2.86592 7.3 2.86790 2.86987 2.87184 2.87381 2.87578 2.87774 2.87971 2.88166 2.88362 2.88557 7.4 2.88753 2.88947 2.89142 2.89336 2.89530 2.89724 2.89918 2.90111 2.90304 2.90497 7.5 2.90689 2.90881 2.91073 2.91265 2.91456 2.91648 2.91839 2.92029 2.92220 2.92410 7.6 2.92600 2.92790 2.92979 2.93168 2.93357 2.93546 2.93734 2.93923 2.94111 2.94298 7.7 2.94486 2.94673 2.94860 2.95047 2.95233 2.95420 2.95606 2.95791 2.95977 2.96162 7.8 2.96347 2.96532 2.96717 2.96901 2.97085 2.97269 2.97453 2.97636 2.97820 2.98003 7.9 2.98185 2.98368 2.98550 2.98732 2.98914 2.99095 2.99277 2.99458 2.99639 2.99820 N0123456789 8.0 3.00000 3.00180 3.00360 3.00540 3.00720 3.00899 3.01078 3.01257 3.01436 3.01614 8.1 3.01792 3.01970 3.02148 3.02326 3.02503 3.02680 3.02857 3.03034 3.03210 3.03386 8.2 3.03562 3.03738 3.03914 3.04089 3.04264 3.04439 3.04614 3.04789 3.04963 3.05137 8.3 3.05311 3.05485 3.05658 3.05832 3.06005 3.06178 3.06350 3.06523 3.06695 3.06867 8.4 3.07039 3.07211 3.07382 3.07553 3.07724 3.07895 3.08066 3.08236 3.08406 3.08576 8.5 3.08746 3.08916 3.09085 3.09255 3.09424 3.09592 3.09761 3.09930 3.10098 3.10266 8.6 3.10434 3.10601 3.10769 3.10936 3.11103 3.11270 3.11437 3.11603 3.11770 3.11936 8.7 3.12102 3.12267 3.12433 3.12598 3.12763 3.12928 3.13093 3.13258 3.13422 3.13586 8.8 3.13750 3.13914 3.14078 3.14241 3.14405 3.14568 3.14731 3.14893 3.15056 3.15218 8.9 3.15381 3.15543 3.15704 3.15866 3.16027 3.16189 3.16350 3.16511 3.16672 3.16832 N0123456789 9.0 3.16993 3.17153 3.17313 3.17473 3.17632 3.17792 3.17951 3.18110 3.18269 3.18428 9.1 3.18587 3.18745 3.18903 3.19061 3.19219 3.19377 3.19535 3.19692 3.19849 3.20006 9.2 3.20163 3.20320 3.20477 3.20633 3.20789 3.20945 3.21101 3.21257 3.21412 3.21568 9.3 3.21723 3.21878 3.22033 3.22188 3.22342 3.22497 3.22651 3.22805 3.22959 3.23113 9.4 3.23266 3.23419 3.23573 3.23726 3.23879 3.24031 3.24184 3.24336 3.24489 3.24641 9.5 3.24793 3.24945 3.25096 3.25248 3.25399 3.25550 3.25701 3.25852 3.26003 3.26153 9.6 3.26303 3.26454 3.26604 3.26754 3.26903 3.27053 3.27202 3.27352 3.27501 3.27650 9.7 3.27798 3.27947 3.28096 3.28244 3.28392 3.28540 3.28688 3.28836 3.28983 3.29131 9.8 3.29278 3.29425 3.29572 3.29719 3.29866 3.30012 3.30159 3.30305 3.30451 3.30597

9.9 3.30743 3.30889 3.31034 3.31179 3.31325 3.31470 3.31615 3.31759 3.31904 3.32048

10.03.32193 3.32337 3.32481 3.32625 3.32769 3.32912 3.33056 3.33199 3.33342 3.33485

Common Logarithms Table - log

10

N

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1.65.217484.217747.218010.218273.218536.218798.219060.219323.219585.219846 1.66.220108.220370.220631.220892.221153.221414.221675.221936.222196.222456 1.67.222716.222976.223236.223496.223755.224015.224274.224533.224792.225051 1.68.225309.225568.225826.226084.226342.226600.226858.227115.227372.227630 1.69.227887.228144.228400.228657.228913.229170.229426.229682.229938.230193 1.70.230449.230704.230960.231215.231470.231724.231979.232234.232488.232742 1.71.232996.233250.233504.233757.234011.234264.234517.234770.235023.235276 1.72.235528.235781.236033.236285.236537.236789.237041.237292.237544.237795 1.73.238046.238297.238548.238799.239049.239299.239550.239800.240050.240300 1.74.240549.240799.241048.241297.241546.241795.242044.242293.242541.242790 1.75.243038.243286.243534.243782.244030.244277.244525.244772.245019.245266 1.76.245513.245759.246006.246252.246499.246745.246991.247237.247482.247728 1.77.247973.248219.248464.248709.248954.249198.249443.249687.249932.250176 1.78.250420.250664.250908.251151.251395.251638.251881.252125.252368.252610 1.79.252853.253096.253338.253580.253822.254064.254306.254548.254790.255031 1.80.255273.255514.255755.255996.256237.256477.256718.256958.257198.257439 1.81.257679.257918.258158.258398.258637.258877.259116.259355.259594.259833 1.82.260071.260310.260548.260787.261025.261263.261501.261739.261976.262214 1.83.262451.262688.262925.263162.263399.263636.263873.264109.264346.264582 1.84.264818.265054.265290.265525.265761.265996.266232.266467.266702.266937 1.85.267172.267406.267641.267875.268110.268344.268578.268812.269046.269279 1.86.269513.269746.269980.270213.270446.270679.270912.271144.271377.271609 1.87.271842.272074.272306.272538.272770.273001.273233.273464.273696.273927 1.88.274158.274389.274620.274850.275081.275311.275542.275772.276002.276232 1.89.276462.276692.276921.277151.277380.277609.277838.278067.278296.278525 1.90.278754.278982.279211.279439.279667.279895.280123.280351.280578.280806 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2.04.309630.309843.310056.310268.310481.310693.310906.311118.311330.311542 2.05.311754.311966.312177.312389.312600.312812.313023.313234.313445.313656 2.06.313867.314078.314289.314499.314710.314920.315130.315340.315551.315760 2.07.315970.316180.316390.316599.316809.317018.317227.317436.317646.317854 2.08.318063.318272.318481.318689.318898.319106.319314.319522.319730.319938 2.09.320146.320354.320562.320769.320977.321184.321391.321598.321805.322012

2.10.322219.322426.32263

3.322839.323046.323252.323458.323665.323871.324077 2.11.324282.324488.32469

4.324899.32510

5.325310.32551

6.325721.325926.326131 2.12.326336.326541.326745.326950.327155.327359.327563.32776

7.327972.328176 2.13.328380.328583.328787.328991.329194.32939

8.329601.329805.330008.330211 2.14.330414.330617.33081

9.331022.331225.331427.331630.331832.332034.332236 2.15.332438.332640.332842.333044.333246.333447.333649.333850.334051.334253 2.16.334454.334655.334856.335057.335257.335458.335658.335859.336059.336260 2.17.336460.336660.336860.337060.337260.337459.337659.337858.338058.338257 2.18.338456.338656.338855.339054.339253.339451.339650.339849.340047.340246 2.19.340444.340642.340841.341039.341237.341435.341632.341830.342028.342225

2.20.34242

3.342620.342817.34301

4.343212.343409.343606.343802.343999.344196 2.21.344392.344589.34478

5.344981.345178.345374.345570.34576

6.345962.346157 2.22.346353.346549.346744.346939.347135.347330.347525.347720.347915.348110 2.23.348305.348500.348694.348889.349083.349278.349472.349666.349860.350054 2.24.350248.350442.350636.350829.351023.351216.351410.351603.351796.351989 2.25.352183.352375.352568.352761.352954.35314

7.353339.353532.353724.353916 2.26.35410

8.354301.354493.354685.354876.355068.355260.355452.355643.355834 2.27.356026.356217.356408.35659

9.356790.356981.357172.357363.357554.357744 2.28.357935.358125.358316.358506.358696.358886.359076.359266.359456.359646 2.29.359835.360025.360215.360404.360593.360783.360972.361161.361350.361539 2.30.361728.361917.362105.362294.362482.362671.362859.363048.363236.363424 2.31.363612.363800.363988.364176.364363.364551.364739.364926.365113.365301 2.32.365488.365675.365862.366049.366236.366423.366610.366796.366983.367169 2.33.367356.367542.367729.367915.368101.368287.368473.368659.368845.369030 2.34.369216.369401.369587.369772.369958.370143.370328.370513.370698.370883 2.35.371068.371253.371437.371622.371806.371991.372175.372360.372544.372728 2.36.372912.373096.373280.373464.373647.373831.374015.374198.374382.374565 2.37.374748.374932.375115.375298.375481.375664.375846.376029.376212.376394 2.38.376577.376759.376942.377124.377306.377488.377670.377852.378034.378216 2.39.378398.378580.378761.378943.379124.379306.379487.379668.379849.380030

2.40.380211.380392.38057

3.38075

4.380934.38111

5.38129

6.381476.381656.381837 2.41.38201

7.382197.382377.382557.382737.382917.383097.383277.383456.383636 2.42.383815.383995.384174.384353.384533.384712.384891.385070.385249.385428 2.43.385606.385785.385964.386142.386321.386499.386677.386856.387034.387212 2.44.387390.38756

8.387746.387923.388101.38827

9.388456.388634.388811.388989 2.45.389166.389343.389520.389698.389875.390051.390228.390405.390582.390759 2.46.390935.391112.391288.391464.391641.391817.391993.392169.392345.392521 2.47.392697.392873.393048.393224.393400.393575.393751.393926.394101.394277 2.48.394452.394627.394802.394977.395152.395326.395501.395676.395850.396025 2.49.396199.396374.396548.396722.396896.397071.397245.397419.397592.397766 2.50.397940.398114.398287.398461.398634.398808.398981.399154.399328.399501 2.51.399674.399847.400020.400192.400365.400538.400711.400883.401056.401228 2.52.401401.401573.401745.401917.402089.402261.402433.402605.402777.402949 2.53.403121.403292.403464.403635.403807.403978.404149.404320.404492.404663 2.54.404834.405005.405176.405346.405517.405688.405858.406029.406199.406370 2.55.406540.406710.406881.407051.407221.407391.407561.407731.407901.408070 2.56.408240.408410.408579.408749.408918.409087.409257.409426.409595.409764 2.57.409933.410102.410271.410440.410609.410777.410946.411114.411283.411451 2.58.411620.411788.411956.412124.412293.412461.412629.412796.412964.413132 2.59.413300.413467.413635.413803.413970.414137.414305.414472.414639.414806

2.60.41497

3.415140.415307.41547

4.415641.415808.415974.416141.416308.416474 2.61.416641.416807.416973.417139.417306.417472.417638.417804.417970.418135 2.62.418301.418467.418633.418798.418964.419129.41929

5.419460.419625.419791 2.63.41995

6.420121.420286.420451.420616.420781.420945.421110.421275.421439 2.64.421604.421768.421933.42209

7.422261.422426.422590.422754.42291

8.423082 2.65.423246.423410.423574.423737.423901.424065.424228.424392.424555.424718 2.66.424882.425045.425208.425371.425534.425697.425860.426023.426186.426349 2.67.426511.426674.426836.42699

9.427161.427324.427486.427648.427811.427973 2.68.428135.428297.428459.428621.428783.428944.429106.429268.429429.429591 2.69.429752.429914.430075.430236.430398.430559.430720.430881.431042.431203 2.70.431364.431525.431685.431846.432007.432167.432328.432488.432649.432809 2.71.432969.433130.433290.433450.433610.433770.433930.434090.434249.434409 2.72.434569.434729.434888.435048.435207.435367.435526.435685.435844.436004 2.73.436163.436322.436481.436640.436799.436957.437116.437275.437433.437592 2.74.437751.437909.438067.438226.438384.438542.438701.438859.439017.439175 2.75.439333.439491.439648.439806.439964.440122.440279.440437.440594.440752 2.76.440909.441066.441224.441381.441538.441695.441852.442009.442166.442323 2.77.442480.442637.442793.442950.443106.443263.443419.443576.443732.443889 2.78.444045.444201.444357.444513.444669.444825.444981.445137.445293.445449 2.79.445604.445760.445915.446071.446226.446382.446537.446692.446848.447003

2.80.447158.44731

3.447468.447623.447778.447933.448088.448242.448397.448552 2.81.448706.448861.449015.449170.44932

4.449478.449633.449787.449941.450095 2.82.450249.450403.450557.450711.45086

5.451018.451172.45132

6.451479.451633 2.83.451786.451940.452093.45224

7.452400.452553.452706.452859.453012.453165 2.84.45331

8.453471.453624.453777.453930.454082.454235.454387.454540.454692 2.85.454845.454997.455150.455302.455454.455606.455758.455910.456062.456214 2.86.456366.456518.456670.456821.456973.457125.457276.457428.45757

9.457731 2.87.457882.458033.458184.458336.458487.458638.458789.458940.459091.459242 2.88.459392.459543.459694.459845.459995.460146.460296.460447.460597.460748 2.89.460898.461048.461198.461348.461499.461649.461799.461948.462098.462248 2.90.462398.462548.462697.462847.462997.463146.463296.463445.463594.463744 2.91.463893.464042.464191.464340.464490.464639.464788.464936.465085.465234 2.92.465383.465532.465680.465829.465977.466126.466274.466423.466571.466719 2.93.466868.467016.467164.467312.467460.467608.467756.467904.468052.468200 2.94.468347.468495.468643.468790.468938.469085.469233.469380.469527.469675 2.95.469822.469969.470116.470263.470410.470557.470704.470851.470998.471145 2.96.471292.471438.471585.471732.471878.472025.472171.472318.472464.472610 2.97.472756.472903.473049.473195.473341.473487.473633.473779.473925.474071 2.98.474216.474362.474508.474653.474799.474944.475090.475235.475381.475526 2.99.475671.475816.475962.476107.476252.476397.476542.476687.476832.476976

3.00.477121.477266.477411.477555.477700.47784

4.477989.478133.478278.478422 3.01.478566.478711.47885

5.478999.479143.479287.479431.479575.479719.479863 3.02.480007.480151.480294.480438.480582.480725.480869.481012.48115

6.481299 3.03.481443.481586.481729.481872.482016.482159.482302.482445.482588.482731 3.04.482874.483016.483159.483302.483445.48358

7.483730.483872.484015.484157 3.05.484300.484442.484585.484727.484869.485011.485153.485295.485437.485579 3.06.485721.485863.486005.486147.486289.486430.486572.486714.486855.486997 3.07.48713

8.487280.487421.487563.487704.487845.487986.488127.48826

9.488410 3.08.488551.488692.488833.488974.489114.489255.489396.489537.489677.489818 3.09.489958.490099.490239.490380.490520.490661.490801.490941.491081.491222 3.10.491362.491502.491642.491782.491922.492062.492201.492341.492481.492621 3.11.492760.492900.493040.493179.493319.493458.493597.493737.493876.494015 3.12.494155.494294.494433.494572.494711.494850.494989.495128.495267.495406 3.13.495544.495683.495822.495960.496099.496238.496376.496515.496653.496791 3.14.496930.497068.497206.497344.497483.497621.497759.497897.498035.498173

3.15.498311.498448.498586.49872

4.498862.498999.499137.49927

5.499412.499550 3.1

6.49968

7.499824.499962.500099.500236.500374.500511.50064

8.500785.500922 3.17.50105

9.501196.501333.501470.501607.501744.501880.502017.502154.502291 3.18.502427.502564.502700.502837.502973.503109.503246.503382.503518.503655 3.19.503791.503927.504063.504199.504335.504471.504607.504743.504878.505014

3.20.505150.505286.505421.505557.505693.505828.50596

4.506099.506234.506370 3.21.50650

5.506640.50677

6.506911.507046.507181.507316.507451.507586.507721 3.22.507856.507991.508126.508260.508395.508530.508664.508799.508934.509068 3.23.509203.50933

7.509471.509606.509740.509874.510009.510143.510277.510411 3.24.510545.510679.510813.510947.511081.511215.511349.511482.511616.511750 3.25.511883.512017.512151.512284.51241

8.512551.512684.512818.512951.513084 3.26.513218.513351.513484.513617.513750.513883.514016.51414

9.514282.514415 3.27.514548.514681.514813.514946.515079.515211.515344.515476.515609.515741 3.28.515874.516006.516139.516271.516403.516535.516668.516800.516932.517064 3.29.517196.517328.517460.517592.517724.517855.517987.518119.518251.518382

3.30.51851

4.518646.518777.518909.519040.519171.519303.519434.519566.519697 3.31.519828.519959.520090.520221.520353.520484.52061

5.520745.52087

6.521007 3.32.521138.521269.521400.521530.521661.521792.521922.522053.522183.522314 3.33.522444.522575.522705.522835.522966.523096.523226.523356.523486.523616 3.34.523746.523876.524006.524136.524266.524396.524526.524656.524785.524915 3.35.525045.525174.525304.525434.525563.525693.525822.525951.526081.526210 3.36.526339.526469.526598.52672

7.526856.526985.527114.527243.527372.527501 3.37.527630.527759.52788

8.528016.528145.528274.528402.528531.528660.528788 3.38.528917.529045.529174.529302.529430.52955

9.529687.529815.529943.530072 3.39.530200.530328.530456.530584.530712.530840.530968.531096.531223.531351 3.40.531479.531607.531734.531862.531990.532117.532245.532372.532500.532627 3.41.532754.532882.533009.533136.533264.533391.533518.533645.533772.533899 3.42.534026.534153.534280.534407.534534.534661.534787.534914.535041.535167 3.43.535294.535421.535547.535674.535800.535927.536053.536180.536306.536432 3.44.536558.536685.536811.536937.537063.537189.537315.537441.537567.537693 3.45.537819.537945.538071.538197.538322.538448.538574.538699.538825.538951 3.46.539076.539202.539327.539452.539578.539703.539829.539954.540079.540204 3.47.540329.540455.540580.540705.540830.540955.541080.541205.541330.541454 3.48.541579.541704.541829.541953.542078.542203.542327.542452.542576.542701 3.49.542825.542950.543074.543199.543323.543447.543571.543696.543820.543944

3.50.544068.544192.544316.544440.54456

4.544688.544812.544936.545060.545183 3.51.545307.545431.54555

5.545678.545802.545925.546049.546172.54629

6.546419 3.52.546543.546666.546789.546913.547036.547159.547282.547405.547529.547652 3.53.547775.547898.548021.548144.54826

7.548389.548512.548635.54875

8.548881 3.54.549003.549126.54924

9.549371.549494.549616.549739.549861.549984.550106 3.55.550228.550351.550473.550595.550717.550840.550962.551084.551206.551328 3.56.551450.551572.551694.551816.551938.552060.552181.552303.552425.552547 3.57.552668.552790.552911.553033.553155.553276.553398.553519.553640.553762 3.58.553883.554004.554126.554247.554368.554489.554610.554731.554852.554973 3.59.555094.555215.555336.555457.555578.555699.555820.555940.556061.556182 3.60.556303.556423.556544.556664.556785.556905.557026.557146.557267.557387 3.61.557507.557627.557748.557868.557988.558108.558228.558349.558469.558589 3.62.558709.558829.558948.559068.559188.559308.559428.559548.559667.559787 3.63.559907.560026.560146.560265.560385.560504.560624.560743.560863.560982 3.64.561101.561221.561340.561459.561578.561698.561817.561936.562055.562174 3.65.562293.562412.562531.562650.562769.562887.563006.563125.563244.563362 3.66.563481.563600.563718.563837.563955.564074.564192.564311.564429.564548 3.67.564666.564784.564903.565021.565139.565257.565376.565494.565612.565730 3.68.565848.565966.566084.566202.566320.566437.566555.566673.566791.566909 3.69.567026.567144.567262.567379.567497.567614.567732.567849.567967.568084

3.70.568202.568319.568436.56855

4.568671.568788.56890

5.569023.569140.569257 3.71.569374.569491.569608.569725.569842.569959.57007

6.570193.570309.570426 3.72.570543.570660.570776.570893.571010.571126.571243.571359.571476.571592 3.73.571709.571825.571942.572058.572174.572291.57240

7.572523.572639.572755 3.74.572872.57298

8.573104.573220.573336.573452.573568.573684.573800.573915 3.75.574031.574147.574263.57437

9.574494.574610.574726.574841.574957.575072 3.76.575188.575303.575419.575534.575650.575765.575880.575996.576111.576226 3.77.576341.576457.576572.576687.576802.576917.577032.577147.577262.577377 3.78.577492.577607.577722.577836.577951.578066.578181.578295.578410.578525 3.79.578639.578754.578868.578983.579097.579212.579326.579441.579555.579669 3.80.579784.579898.580012.580126.580241.580355.580469.580583.580697.580811 3.81.580925.581039.581153.581267.581381.581495.581608.581722.581836.581950 3.82.582063.582177.582291.582404.582518.582631.582745.582858.582972.583085 3.83.583199.583312.583426.583539.583652.583765.583879.583992.584105.584218 3.84.584331.584444.584557.584670.584783.584896.585009.585122.585235.585348 3.85.585461.585574.585686.585799.585912.586024.586137.586250.586362.586475 3.86.586587.586700.586812.586925.587037.587149.587262.587374.587486.587599 3.87.587711.587823.587935.588047.588160.588272.588384.588496.588608.588720 3.88.588832.588944.589056.589167.589279.589391.589503.589615.589726.589838 3.89.589950.590061.590173.590284.590396.590507.590619.590730.590842.590953

3.90.591065.591176.591287.591399.591510.591621.591732.591843.591955.592066 3.91.592177.592288.592399.592510.592621.592732.592843.59295

4.593064.593175 3.92.593286.593397.593508.593618.593729.593840.593950.594061.594171.594282 3.93.594393.594503.594614.594724.594834.59494

5.595055.595165.59527

6.595386 3.94.595496.595606.59571

7.595827.595937.596047.596157.596267.596377.596487 3.95.596597.596707.596817.596927.597037.597146.597256.597366.597476.597586 3.96.597695.597805.597914.598024.598134.598243.598353.598462.598572.598681 3.97.598791.598900.599009.599119.59922

8.599337.599446.599556.599665.599774 3.98.599883.599992.600101.600210.60031

9.600428.600537.600646.600755.600864

3.99.600973.601082.601191.601299.601408.601517.601625.60173

4.601843.601951

4.00.602060.602169.602277.602386.602494.602603.602711.602819.602928.603036 4.01.603144.603253.603361.603469.603577.603686.603794.603902.604010.604118 4.02.604226.604334.604442.604550.604658.604766.604874.604982.605089.605197 4.03.60530

5.605413.605521.605628.60573

6.605844.605951.606059.606166.606274 4.04.606381.606489.606596.606704.606811.606919.607026.607133.607241.607348 4.05.607455.607562.607669.60777

7.607884.607991.60809

8.608205.608312.608419 4.06.608526.608633.608740.608847.608954.609061.609167.609274.609381.609488 4.07.609594.609701.609808.609914.610021.610128.610234.610341.610447.610554 4.08.610660.610767.610873.61097

9.611086.611192.611298.611405.611511.611617 4.09.611723.611829.611936.612042.612148.612254.612360.612466.612572.612678 4.10.612784.612890.612996.613102.613207.613313.613419.613525.613630.613736 4.11.613842.613947.614053.614159.614264.614370.614475.614581.614686.614792 4.12.614897.615003.615108.615213.615319.615424.615529.615634.615740.615845 4.13.615950.616055.616160.616265.616370.616476.616581.616686.616790.616895 4.14.617000.617105.617210.617315.617420.617525.617629.617734.617839.617943 4.15.618048.618153.618257.618362.618466.618571.618676.618780.618884.618989 4.16.619093.619198.619302.619406.619511.619615.619719.619824.619928.620032 4.17.620136.620240.620344.620448.620552.620656.620760.620864.620968.621072 4.18.621176.621280.621384.621488.621592.621695.621799.621903.622007.622110 4.19.622214.622318.622421.622525.622628.622732.622835.622939.623042.623146

4.20.623249.623353.623456.623559.623663.623766.623869.623973.624076.624179 4.21.624282.62438

5.624488.624591.624695.624798.624901.625004.625107.625210 4.22.625312.625415.625518.625621.625724.625827.625929.626032.626135.626238 4.23.626340.626443.62654

6.626648.626751.626853.626956.627058.627161.627263 4.24.627366.627468.627571.627673.627775.627878.627980.628082.628185.628287 4.25.628389.628491.628593.628695.62879

7.628900.629002.629104.629206.629308 4.26.629410.629512.629613.629715.629817.629919.630021.630123.630224.630326 4.27.63042

8.630530.630631.630733.630835.630936.631038.63113

9.631241.631342 4.28.631444.631545.631647.631748.631849.631951.632052.632153.632255.632356 4.29.632457.632559.632660.632761.632862.632963.633064.633165.633266.6333674.30.633468.633569.633670.633771.633872.633973.634074.634175.634276.634376 4.31.634477.634578.634679.634779.634880.634981.635081.635182.635283.635383 4.32.635484.635584.635685.635785.635886.635986.636087.636187.636287.636388 4.33.636488.636588.636688.636789.636889.636989.637089.637189.637290.637390 4.34.637490.637590.637690.637790.637890.637990.638090.638190.638290.638389 4.35.638489.638589.638689.638789.638888.638988.639088.639188.639287.639387 4.36.639486.639586.639686.639785.639885.639984.640084.640183.640283.640382 4.37.640481.640581.640680.640779.640879.640978.641077.641177.641276.641375 4.38.641474.641573.641672.641771.641871.641970.642069.642168.642267.642366 4.39.642465.642563.642662.642761.642860.642959.643058.643156.643255.643354

4.40.643453.643551.643650.643749.643847.643946.644044.644143.644242.644340 4.41.644439.644537.644636.644734.644832.644931.645029.645127.645226.645324 4.42.645422.645521.645619.645717.64581

5.645913.646011.646110.646208.646306 4.43.646404.646502.646600.646698.64679

6.646894.646992.647089.64718

7.647285 4.44.647383.647481.647579.647676.647774.647872.647969.648067.648165.648262 4.45.648360.64845

8.648555.648653.648750.648848.648945.649043.649140.649237 4.46.649335.649432.649530.649627.649724.649821.64991

9.650016.650113.650210 4.47.650308.650405.650502.650599.650696.650793.650890.650987.651084.651181 4.48.651278.651375.651472.651569.651666.651762.651859.651956.652053.652150 4.49.652246.652343.652440.652536.652633.652730.652826.652923.653019.653116

4.50.653213.653309.65340

5.653502.653598.653695.653791.653888.653984.654080 4.51.654177.654273.654369.654465.654562.654658.654754.654850.65494

6.655042 4.52.655138.655235.655331.65542

7.655523.655619.655715.655810.655906.656002 4.53.65609

8.656194.656290.656386.656482.656577.656673.65676

9.656864.656960 4.54.657056.657152.657247.657343.657438.657534.657629.657725.657820.657916 4.55.658011.658107.658202.658298.658393.658488.658584.658679.658774.658870 4.56.658965.659060.659155.659250.659346.659441.659536.659631.659726.659821 4.57.659916.660011.660106.660201.660296.660391.660486.660581.660676.660771 4.58.660865.660960.661055.661150.661245.661339.661434.661529.661623.661718 4.59.661813.661907.662002.662096.662191.662286.662380.662475.662569.662663 4.60.662758.662852.662947.663041.663135.663230.663324.663418.663512.663607 4.61.663701.663795.663889.663983.664078.664172.664266.664360.664454.664548 4.62.664642.664736.664830.664924.665018.665112.665206.665299.665393.665487 4.63.665581.665675.665769.665862.665956.666050.666143.666237.666331.666424 4.64.666518.666612.666705.666799.666892.666986.667079.667173.667266.667360 4.65.667453.667546.667640.667733.667826.667920.668013.668106.668199.668293 4.66.668386.668479.668572.668665.668759.668852.668945.669038.669131.669224 4.67.669317.669410.669503.669596.669689.669782.669875.669967.670060.670153 4.68.670246.670339.670431.670524.670617.670710.670802.670895.670988.671080 4.69.671173.671265.671358.671451.671543.671636.671728.671821.671913.672005

4.70.672098.672190.672283.67237

5.672467.672560.672652.672744.67283

6.672929 4.71.673021.673113.673205.67329

7.673390.673482.673574.673666.67375

8.673850 4.72.673942.674034.674126.674218.674310.674402.674494.674586.674677.674769 4.73.674861.674953.675045.675137.675228.675320.675412.675503.675595.675687 4.74.675778.675870.675962.676053.676145.676236.676328.67641

9.676511.676602 4.75.676694.676785.676876.676968.677059.677151.677242.677333.677424.677516 4.76.677607.677698.677789.677881.677972.678063.678154.678245.678336.678427 4.77.678518.678609.678700.678791.678882.678973.679064.679155.679246.679337 4.78.679428.679519.679610.679700.679791.679882.679973.680063.680154.680245 4.79.680336.680426.680517.680607.680698.680789.680879.680970.681060.681151 4.80.681241.681332.681422.681513.681603.681693.681784.681874.681964.682055 4.81.682145.682235.682326.682416.682506.682596.682686.682777.682867.682957 4.82.683047.683137.683227.683317.683407.683497.683587.683677.683767.683857 4.83.683947.684037.684127.684217.684307.684396.684486.684576.684666.684756 4.84.684845.684935.685025.685114.685204.685294.685383.685473.685563.685652 4.85.685742.685831.685921.686010.686100.686189.686279.686368.686458.686547 4.86.686636.686726.686815.686904.686994.687083.687172.687261.687351.687440 4.87.687529.687618.687707.687796.687886.687975.688064.688153.688242.688331 4.88.688420.688509.688598.688687.688776.688865.688953.689042.689131.689220 4.89.689309.689398.689486.689575.689664.689753.689841.689930.690019.690107

4.90.690196.69028

5.690373.690462.690550.690639.690728.69081

6.690905.690993 4.91.691081.691170.691258.69134

7.691435.691524.691612.691700.691789.691877 4.92.691965.692053.692142.692230.69231

8.692406.692494.692583.692671.692759 4.93.692847.692935.693023.693111.69319

9.693287.693375.693463.693551.693639 4.94.693727.693815.693903.693991.694078.694166.694254.694342.694430.694517 4.95.694605.694693.694781.694868.694956.695044.695131.695219.695307.695394 4.96.695482.695569.695657.695744.695832.695919.696007.696094.696182.696269 4.97.696356.696444.696531.696618.696706.696793.696880.696968.697055.697142 4.98.697229.697317.697404.697491.697578.697665.697752.697839.697926.698014

4.99.698101.698188.69827

5.698362.698449.698535.698622.698709.69879

6.698883

5.00.698970.699057.699144.699231.699317.699404.699491.699578.699664.699751 5.01.699838.699924.700011.700098.700184.700271.700358.700444.700531.700617 5.02.700704.700790.700877.700963.701050.70113

6.701222.701309.701395.701482 5.03.701568.701654.701741.70182

7.701913.701999.702086.702172.70225

8.702344 5.04.702431.702517.702603.70268

9.702775.702861.702947.703033.703119.703205 5.05.703291.703377.703463.703549.703635.703721.703807.703893.703979.704065 5.06.704151.704236.704322.704408.704494.704579.704665.704751.704837.704922 5.07.705008.705094.705179.705265.705350.705436.705522.705607.705693.705778 5.08.705864.705949.706035.706120.706206.706291.706376.706462.706547.706632 5.09.706718.706803.706888.706974.707059.707144.707229.707315.707400.707485 5.10.707570.707655.707740.707826.707911.707996.708081.708166.708251.708336 5.11.708421.708506.708591.708676.708761.708846.708931.709015.709100.709185 5.12.709270.709355.709440.709524.709609.709694.709779.709863.709948.710033 5.13.710117.710202.710287.710371.710456.710540.710625.710710.710794.710879 5.14.710963.711048.711132.711217.711301.711385.711470.711554.711639.711723 5.15.711807.711892.711976.712060.712144.712229.712313.712397.712481.712566 5.16.712650.712734.712818.712902.712986.713070.713154.713238.713323.713407 5.17.713491.713575.713659.713742.713826.713910.713994.714078.714162.714246 5.18.714330.714414.714497.714581.714665.714749.714833.714916.715000.715084 5.19.715167.715251.715335.715418.715502.715586.715669.715753.715836.715920

5.20.716003.716087.716170.716254.716337.716421.716504.716588.716671.716754 5.21.716838.716921.717004.717088.717171.717254.717338.717421.717504.717587 5.22.717671.717754.717837.717920.718003.71808

6.718169.718253.718336.718419 5.23.718502.718585.718668.718751.718834.71891

7.719000.719083.719165.719248 5.24.719331.719414.719497.719580.719663.719745.71982

8.719911.719994.720077 5.25.72015

9.720242.720325.720407.720490.720573.720655.720738.720821.720903 5.26.720986.721068.721151.721233.721316.721398.721481.721563.721646.721728 5.27.721811.721893.721975.722058.722140.722222.722305.722387.722469.722552 5.28.722634.722716.722798.722881.722963.723045.723127.723209.723291.723374 5.29.723456.723538.723620.723702.723784.723866.723948.724030.724112.724194 5.30.724276.724358.724440.724522.724604.724685.724767.724849.724931.725013 5.31.725095.725176.725258.725340.725422.725503.725585.725667.725748.725830 5.32.725912.725993.726075.726156.726238.726320.726401.726483.726564.726646 5.33.726727.726809.726890.726972.727053.727134.727216.727297.727379.727460 5.34.727541.727623.727704.727785.727866.727948.728029.728110.728191.728273 5.35.728354.728435.728516.728597.728678.728759.728841.728922.729003.729084 5.36.729165.729246.729327.729408.729489.729570.729651.729732.729813.729893 5.37.729974.730055.730136.730217.730298.730378.730459.730540.730621.730702 5.38.730782.730863.730944.731024.731105.731186.731266.731347.731428.731508 5.39.731589.731669.731750.731830.731911.731991.732072.732152.732233.732313

5.40.732394.732474.732555.732635.732715.73279

6.732876.732956.73303

7.733117 5.41.733197.73327

8.733358.733438.733518.733598.73367

9.733759.733839.733919 5.42.733999.734079.734160.734240.734320.734400.734480.734560.734640.734720 5.43.734800.734880.734960.735040.735120.735200.735279.735359.735439.735519

5.44.735599.735679.735759.735838.735918.735998.736078.736157.736237.736317 5.45.736397.73647

6.736556.736635.736715.736795.736874.736954.737034.737113 5.46.737193.737272.737352.737431.737511.737590.737670.737749.737829.737908 5.4

7.737987.738067.738146.738225.738305.738384.738463.738543.738622.738701 5.4

8.738781.738860.73893

9.739018.739097.739177.739256.739335.739414.739493 5.49.739572.739651.739731.739810.739889.739968.740047.740126.740205.740284

5.50.740363.740442.740521.740600.740678.740757.74083

6.740915.740994.741073 5.51.741152.741230.741309.741388.74146

7.741546.741624.741703.741782.741860 5.52.741939.74201

8.742096.742175.742254.742332.742411.74248

9.742568.742647 5.53.742725.742804.742882.742961.743039.743118.743196.743275.743353.743431 5.54.743510.743588.743667.743745.743823.743902.743980.744058.744136.744215 5.55.744293.744371.744449.744528.744606.744684.744762.744840.744919.744997 5.56.745075.745153.745231.745309.745387.745465.745543.745621.745699.745777 5.57.745855.745933.746011.746089.746167.746245.746323.746401.746479.746556 5.58.746634.746712.746790.746868.746945.747023.747101.747179.747256.747334 5.59.747412.747489.747567.747645.747722.747800.747878.747955.748033.748110

5.60.748188.74826

6.748343.748421.748498.748576.748653.748731.748808.748885 5.61.748963.749040.749118.749195.749272.749350.74942

7.749504.749582.749659 5.62.749736.749814.749891.74996

8.750045.750123.750200.750277.750354.750431 5.63.750508.750586.750663.750740.750817.750894.750971.751048.751125.751202 5.64.75127

9.751356.751433.751510.751587.751664.751741.751818.751895.751972 5.65.752048.752125.752202.752279.752356.752433.752509.752586.752663.752740 5.66.752816.752893.752970.753047.753123.753200.753277.753353.753430.753506 5.67.753583.753660.753736.753813.753889.753966.754042.754119.754195.754272 5.68.754348.754425.754501.754578.754654.754730.754807.754883.754960.755036 5.69.755112.755189.755265.755341.755417.755494.755570.755646.755722.755799 5.70.755875.755951.756027.756103.756180.756256.756332.756408.756484.756560 5.71.756636.756712.756788.756864.756940.757016.757092.757168.757244.757320 5.72.757396.757472.757548.757624.757700.757775.757851.757927.758003.758079 5.73.758155.758230.758306.758382.758458.758533.758609.758685.758761.758836 5.74.758912.758988.759063.759139.759214.759290.759366.759441.759517.759592 5.75.759668.759743.759819.759894.759970.760045.760121.760196.760272.760347 5.76.760422.760498.760573.760649.760724.760799.760875.760950.761025.761101 5.77.761176.761251.761326.761402.761477.761552.761627.761702.761778.761853 5.78.761928.762003.762078.762153.762228.762303.762378.762453.762529.762604 5.79.762679.762754.762829.762904.762978.763053.763128.763203.763278.763353

5.80.763428.763503.763578.763653.763727.763802.763877.763952.764027.764101 5.81.76417

6.764251.764326.764400.764475.764550.764624.764699.764774.764848 5.82.764923.764998.765072.76514

7.765221.765296.765370.765445.765520.765594 5.83.765669.765743.76581

8.765892.765966.766041.766115.766190.766264.766338 5.84.766413.766487.766562.766636.766710.766785.76685

9.766933.767007.767082 5.85.767156.767230.767304.767379.767453.767527.767601.767675.767749.767823 5.86.767898.767972.768046.768120.768194.768268.768342.768416.768490.768564 5.87.768638.768712.768786.768860.768934.769008.769082.769156.769230.769303 5.88.769377.769451.769525.769599.769673.769746.769820.769894.769968.770042 5.89.770115.770189.770263.770336.770410.770484.770557.770631.770705.770778 5.90.770852.770926.770999.771073.771146.771220.771293.771367.771440.771514 5.91.771587.771661.771734.771808.771881.771955.772028.772102.772175.772248 5.92.772322.772395.772468.772542.772615.772688.772762.772835.772908.772981 5.93.773055.773128.773201.773274.773348.773421.773494.773567.773640.773713 5.94.773786.773860.773933.774006.774079.774152.774225.774298.774371.774444 5.95.774517.774590.774663.774736.774809.774882.774955.775028.775100.775173 5.96.775246.775319.775392.775465.775538.775610.775683.775756.775829.775902 5.97.775974.776047.776120.776193.776265.776338.776411.776483.776556.776629 5.98.776701.776774.776846.776919.776992.777064.777137.777209.777282.777354 5.99.777427.777499.777572.777644.777717.777789.777862.777934.778006.778079

6.00.778151.778224.778296.778368.778441.778513.778585.778658.778730.778802 6.01.778874.77894

7.779019.779091.779163.779236.77930

8.779380.779452.779524 6.02.779596.77966

9.779741.779813.779885.779957.780029.780101.780173.780245 6.03.780317.780389.780461.780533.780605.780677.780749.780821.780893.780965 6.04.781037.781109.781181.781253.781324.781396.781468.781540.781612.781684 6.05.781755.781827.781899.781971.782042.782114.782186.782258.782329.782401 6.06.782473.782544.782616.782688.782759.782831.782902.782974.783046.783117 6.07.783189.783260.783332.783403.783475.783546.783618.783689.783761.783832 6.08.783904.783975.784046.784118.784189.784261.784332.784403.784475.784546 6.09.784617.784689.784760.784831.784902.784974.785045.785116.785187.785259 6.10.785330.785401.785472.785543.785615.785686.785757.785828.785899.785970 6.11.786041.786112.786183.786254.786325.786396.786467.786538.786609.786680 6.12.786751.786822.786893.786964.787035.787106.787177.787248.787319.787390 6.13.787460.787531.787602.787673.787744.787815.787885.787956.788027.788098 6.14.788168.788239.788310.788381.788451.788522.788593.788663.788734.788804 6.15.788875.788946.789016.789087.789157.789228.789299.789369.789440.789510 6.16.789581.789651.789722.789792.789863.789933.790004.790074.790144.790215 6.17.790285.790356.790426.790496.790567.790637.790707.790778.790848.790918 6.18.790988.791059.791129.791199.791269.791340.791410.791480.791550.791620 6.19.791691.791761.791831.791901.791971.792041.792111.792181.792252.792322

6.20.792392.792462.792532.792602.792672.792742.792812.792882.792952.793022 6.21.793092.793162.793231.793301.793371.793441.793511.793581.793651.793721 6.22.793790.793860.793930.794000.794070.794139.794209.794279.794349.794418 6.23.794488.794558.79462

7.794697.794767.794836.794906.794976.795045.795115 6.24.795185.795254.795324.795393.795463.795532.795602.795672.795741.795811 6.25.795880.795949.796019.79608

8.796158.796227.796297.796366.796436.796505 6.26.796574.796644.796713.796782.796852.796921.796990.797060.79712

9.797198 6.27.797268.797337.797406.797475.797545.797614.797683.797752.797821.797890 6.28.797960.798029.798098.798167.798236.798305.798374.798443.798513.798582 6.29.798651.798720.798789.798858.798927.798996.799065.799134.799203.799272 6.30.799341.799409.799478.799547.799616.799685.799754.799823.799892.799961 6.31.800029.800098.800167.800236.800305.800373.800442.800511.800580.800648 6.32.800717.800786.800854.800923.800992.801061.801129.801198.801266.801335 6.33.801404.801472.801541.801609.801678.801747.801815.801884.801952.802021 6.34.802089.802158.802226.802295.802363.802432.802500.802568.802637.802705 6.35.802774.802842.802910.802979.803047.803116.803184.803252.803321.803389 6.36.803457.803525.803594.803662.803730.803798.803867.803935.804003.804071 6.37.804139.804208.804276.804344.804412.804480.804548.804616.804685.804753 6.38.804821.804889.804957.805025.805093.805161.805229.805297.805365.805433 6.39.805501.805569.805637.805705.805773.805841.805908.805976.806044.806112

6.40.806180.806248.806316.806384.806451.806519.80658

7.806655.806723.806790 6.41.80685

8.806926.806994.807061.80712

9.807197.807264.807332.807400.807467 6.42.807535.807603.807670.807738.807806.807873.807941.808008.808076.808143 6.43.808211.808279.808346.808414.808481.808549.808616.808684.808751.808818 6.44.808886.808953.809021.809088.809156.809223.809290.809358.809425.809492 6.45.809560.809627.809694.809762.809829.809896.809964.810031.810098.810165 6.46.810233.810300.810367.810434.810501.810569.810636.810703.810770.810837 6.47.810904.810971.811039.811106.811173.811240.811307.811374.811441.811508 6.48.811575.811642.811709.811776.811843.811910.811977.812044.812111.812178 6.49.812245.812312.812379.812445.812512.812579.812646.812713.812780.812847 6.50.812913.812980.813047.813114.813181.813247.813314.813381.813448.813514 6.51.813581.813648.813714.813781.813848.813914.813981.814048.814114.814181 6.52.814248.814314.814381.814447.814514.814581.814647.814714.814780.814847 6.53.814913.814980.815046.815113.815179.815246.815312.815378.815445.815511 6.54.815578.815644.815711.815777.815843.815910.815976.816042.816109.816175 6.55.816241.816308.816374.816440.816506.816573.816639.816705.816771.816838 6.56.816904.816970.817036.817102.817169.817235.817301.817367.817433.817499 6.57.817565.817631.817698.817764.817830.817896.817962.818028.818094.818160 6.58.818226.818292.818358.818424.818490.818556.818622.818688.818754.8188206.60.819544.819610.819676.819741.819807.819873.819939.820004.820070.820136 6.61.820201.820267.820333.820399.820464.820530.820595.820661.820727.820792 6.62.820858.820924.820989.821055.821120.821186.821251.821317.821382.821448 6.63.821514.821579.821645.821710.821775.821841.821906.821972.822037.822103 6.64.822168.822233.822299.822364.822430.822495.822560.822626.822691.822756 6.65.822822.822887.822952.823018.823083.823148.823213.823279.823344.823409 6.66.823474.823539.823605.823670.823735.823800.823865.823930.823996.824061 6.67.824126.824191.824256.824321.824386.824451.824516.824581.824646.824711 6.68.824776.824841.824906.824971.825036.825101.825166.825231.825296.825361 6.69.825426.825491.825556.825621.825686.825751.825815.825880.825945.826010

6.70.826075.826140.826204.826269.826334.826399.826464.826528.826593.826658 6.71.826723.82678

7.826852.826917.826981.827046.827111.827175.827240.827305 6.72.827369.827434.827499.827563.82762

8.827692.827757.827821.827886.827951 6.73.828015.828080.828144.82820

9.828273.828338.828402.828467.828531.828595 6.74.828660.828724.828789.828853.828918.828982.829046.829111.829175.829239 6.75.829304.829368.829432.829497.829561.829625.829690.829754.829818.829882 6.76.829947.830011.830075.830139.830204.830268.830332.830396.830460.830525 6.77.830589.830653.830717.830781.830845.830909.830973.831037.831102.831166 6.78.831230.831294.831358.831422.831486.831550.831614.831678.831742.831806 6.79.831870.831934.831998.832062.832126.832189.832253.832317.832381.832445

6.80.832509.832573.83263

7.832700.832764.83282

8.832892.832956.833020.833083 6.81.833147.833211.833275.833338.833402.833466.833530.833593.833657.833721 6.82.833784.833848.833912.833975.83403

9.834103.834166.834230.834294.834357 6.83.834421.834484.834548.834611.834675.834739.834802.834866.834929.834993 6.84.835056.835120.835183.835247.835310.835373.835437.835500.835564.835627 6.85.835691.835754.835817.835881.835944.836007.836071.836134.836197.836261 6.86.836324.836387.836451.836514.836577.836641.836704.836767.836830.836894 6.87.836957.837020.837083.837146.837210.837273.837336.837399.837462.837525 6.88.837588.837652.837715.837778.837841.837904.837967.838030.838093.838156 6.89.838219.838282.838345.838408.838471.838534.838597.838660.838723.838786 6.90.838849.838912.838975.839038.839101.839164.839227.839289.839352.839415 6.91.839478.839541.839604.839667.839729.839792.839855.839918.839981.840043 6.92.840106.840169.840232.840294.840357.840420.840482.840545.840608.840671 6.93.840733.840796.840859.840921.840984.841046.841109.841172.841234.841297 6.94.841359.841422.841485.841547.841610.841672.841735.841797.841860.841922 6.95.841985.842047.842110.842172.842235.842297.842360.842422.842484.842547 6.96.842609.842672.842734.842796.842859.842921.842983.843046.843108.843170 6.97.843233.843295.843357.843420.843482.843544.843606.843669.843731.843793 6.98.843855.843918.843980.844042.844104.844166.844229.844291.844353.844415 6.99.844477.844539.844601.844664.844726.844788.844850.844912.844974.845036

7.00.845098.845160.845222.845284.845346.845408.845470.845532.845594.845656 7.01.845718.845780.845842.845904.845966.846028.846090.846151.846213.846275 7.02.846337.846399.846461.846523.846585.846646.846708.846770.846832.846894 7.03.846955.847017.847079.847141.847202.847264.847326.847388.847449.847511 7.04.847573.847634.847696.847758.847819.847881.847943.848004.848066.848128 7.05.848189.848251.848312.848374.848435.848497.848559.848620.848682.848743 7.06.848805.848866.848928.848989.849051.849112.849174.849235.849297.849358 7.07.849419.849481.849542.849604.849665.849726.849788.849849.849911.849972 7.08.850033.850095.850156.850217.850279.850340.850401.850462.850524.850585 7.09.850646.850707.850769.850830.850891.850952.851014.851075.851136.851197 7.10.851258.851320.851381.851442.851503.851564.851625.851686.851747.851809 7.11.851870.851931.851992.852053.852114.852175.852236.852297.852358.852419 7.12.852480.852541.852602.852663.852724.852785.852846.852907.852968.853029 7.13.853090.853150.853211.853272.853333.853394.853455.853516.853577.853637 7.14.853698.853759.853820.853881.853941.854002.854063.854124.854185.854245 7.15.854306.854367.854428.854488.854549.854610.854670.854731.854792.854852 7.16.854913.854974.855034.855095.855156.855216.855277.855337.855398.855459 7.17.855519.855580.855640.855701.855761.855822.855882.855943.856003.856064 7.18.856124.856185.856245.856306.856366.856427.856487.856548.856608.856668 7.19.856729.856789.856850.856910.856970.857031.857091.857152.857212.857272

7.20.857332.857393.857453.857513.857574.857634.857694.857755.857815.857875 7.21.857935.857995.858056.858116.858176.858236.858297.858357.858417.858477 7.22.858537.858597.858657.858718.858778.858838.858898.858958.859018.859078 7.23.859138.859198.859258.859318.859379.859439.859499.859559.859619.859679 7.24.859739.859799.859859.859918.859978.860038.860098.860158.860218.860278 7.25.860338.860398.860458.860518.860578.860637.860697.860757.860817.860877 7.26.860937.860996.861056.861116.861176.861236.861295.861355.861415.861475 7.27.861534.861594.861654.861714.861773.861833.861893.861952.862012.862072 7.28.862131.862191.862251.862310.862370.862430.862489.862549.862608.862668 7.29.862728.862787.862847.862906.862966.863025.863085.863144.863204.863263 7.30.863323.863382.863442.863501.863561.863620.863680.863739.863799.863858 7.31.863917.863977.864036.864096.864155.864214.864274.864333.864392.864452 7.32.864511.864570.864630.864689.864748.864808.864867.864926.864985.865045 7.33.865104.865163.865222.865282.865341.865400.865459.865519.865578.865637 7.34.865696.865755.865814.865874.865933.865992.866051.866110.866169.866228 7.35.866287.866346.866405.866465.866524.866583.866642.866701.866760.866819 7.36.866878.866937.866996.867055.867114.867173.867232.867291.867350.867409 7.37.867467.867526.867585.867644.867703.867762.867821.867880.867939.867998 7.38.868056.868115.868174.868233.868292.868350.868409.868468.868527.868586 7.39.868644.868703.868762.868821.868879.868938.868997.869056.869114.869173

7.40.869232.869290.869349.869408.869466.869525.869584.869642.869701.869760 7.41.869818.869877.869935.869994.870053.870111.870170.870228.870287.870345 7.42.870404.870462.870521.870579.870638.870696.870755.870813.870872.870930 7.43.870989.871047.871106.871164.871223.871281.871339.871398.871456.871515 7.44.871573.871631.871690.871748.871806.871865.871923.871981.872040.872098 7.45.872156.872215.872273.872331.872389.872448.872506.872564.872622.872681 7.46.872739.872797.872855.872913.872972.873030.873088.873146.873204.873262 7.47.873321.873379.873437.873495.873553.873611.873669.873727.873785.873844 7.48.873902.873960.874018.874076.874134.874192.874250.874308.874366.874424 7.49.874482.874540.874598.874656.874714.874772.874830.874888.874945.875003 7.50.875061.875119.875177.875235.875293.875351.875409.875466.875524.875582 7.51.875640.875698.875756.875813.875871.875929.875987.876045.876102.876160 7.52.876218.876276.876333.876391.876449.876507.876564.876622.876680.876737 7.53.876795.876853.876910.876968.877026.877083.877141.877199.877256.877314 7.54.877371.877429.877487.877544.877602.877659.877717.877774.877832.877889 7.55.877947.878004.878062.878119.878177.878234.878292.878349.878407.878464 7.56.878522.878579.878637.878694.878752.878809.878866.878924.878981.879039 7.57.879096.879153.879211.879268.879325.879383.879440.879497.879555.879612 7.58.879669.879726.879784.879841.879898.879956.880013.880070.880127.880185 7.59.880242.880299.880356.880413.880471.880528.880585.880642.880699.880756

7.60.880814.880871.880928.880985.881042.881099.881156.881213.881271.881328 7.61.881385.881442.881499.881556.881613.881670.881727.881784.881841.881898 7.62.881955.882012.882069.882126.882183.882240.882297.882354.882411.882468 7.63.882525.882581.882638.882695.882752.882809.882866.882923.882980.883037 7.64.883093.883150.883207.883264.883321.883377.883434.883491.883548.883605 7.65.883661.883718.883775.883832.883888.883945.884002.884059.884115.884172 7.66.884229.884285.884342.884399.884455.884512.884569.884625.884682.884739 7.67.884795.884852.884909.884965.885022.885078.885135.885192.885248.885305 7.68.885361.885418.885474.885531.885587.885644.885700.885757.885813.885870 7.69.885926.885983.886039.886096.886152.886209.886265.886321.886378.886434 7.70.886491.886547.886604.886660.886716.886773.886829.886885.886942.886998 7.71.887054.887111.887167.887223.887280.887336.887392.887449.887505.887561 7.72.887617.887674.887730.887786.887842.887898.887955.888011.888067.888123

6.59.818885.818951.81901

7.819083.819149.819215.819281.819346.819412.819478

7.73.888179.888236.888292.888348.888404.888460.888516.888573.888629.888685 7.74.888741.888797.888853.888909.888965.889021.889077.889134.889190.889246 7.75.889302.889358.889414.889470.889526.889582.889638.889694.889750.889806 7.76.889862.889918.889974.890030.890086.890141.890197.890253.890309.890365 7.77.890421.890477.890533.890589.890645.890700.890756.890812.890868.890924 7.78.890980.891035.891091.891147.891203.891259.891314.891370.891426.891482 7.79.891537.891593.891649.891705.891760.891816.891872.891928.891983.892039

7.80.892095.892150.892206.892262.892317.892373.892429.892484.892540.892595 7.81.892651.892707.892762.892818.892873.892929.892985.893040.893096.893151 7.82.893207.893262.893318.893373.893429.893484.893540.893595.893651.893706 7.83.893762.893817.893873.893928.893984.894039.894094.894150.894205.894261 7.84.894316.894371.894427.894482.894538.894593.894648.894704.894759.894814 7.85.894870.894925.894980.895036.895091.895146.895201.895257.895312.895367 7.86.895423.895478.895533.895588.895644.895699.895754.895809.895864.895920 7.87.895975.896030.896085.896140.896195.896251.896306.896361.896416.896471 7.88.896526.896581.896636.896692.896747.896802.896857.896912.896967.897022 7.89.897077.897132.897187.897242.897297.897352.897407.897462.897517.897572

7.90.897627.897682.897737.897792.897847.897902.897957.898012.898067.898122 7.91.898176.898231.898286.898341.898396.898451.898506.898561.898615.898670 7.92.898725.898780.898835.898890.898944.898999.899054.899109.899164.899218 7.93.899273.899328.899383.899437.899492.899547.899602.899656.899711.899766 7.94.899821.899875.899930.899985.900039.900094.900149.900203.900258.900312 7.95.900367.900422.900476.900531.900586.900640.900695.900749.900804.900859 7.96.900913.900968.901022.901077.901131.901186.901240.901295.901349.901404 7.97.901458.901513.901567.901622.901676.901731.901785.901840.901894.901948 7.98.902003.902057.902112.902166.902221.902275.902329.902384.902438.902492

7.99.902547.902601.902655.902710.902764.902818.902873.902927.902981.903036

8.00.903090.903144.903199.903253.903307.903361.903416.903470.903524.903578 8.01.903633.903687.903741.903795.903849.903904.903958.904012.904066.904120 8.02.904174.904229.904283.904337.904391.904445.904499.904553.904607.904661 8.03.904716.904770.904824.904878.904932.904986.905040.905094.905148.905202 8.04.905256.905310.905364.905418.905472.905526.905580.905634.905688.905742 8.05.905796.905850.905904.905958.906012.906066.906119.906173.906227.906281 8.06.906335.906389.906443.906497.906551.906604.906658.906712.906766.906820 8.07.906874.906927.906981.907035.907089.907143.907196.907250.907304.907358 8.08.907411.907465.907519.907573.907626.907680.907734.907787.907841.907895 8.09.907949.908002.908056.908110.908163.908217.908270.908324.908378.908431 8.10.908485.908539.908592.908646.908699.908753.908807.908860.908914.908967 8.11.909021.909074.909128.909181.909235.909289.909342.909396.909449.909503 8.12.909556.909610.909663.909716.909770.909823.909877.909930.909984.910037 8.13.910091.910144.910197.910251.910304.910358.910411.910464.910518.910571 8.14.910624.910678.910731.910784.910838.910891.910944.910998.911051.911104 8.15.911158.911211.911264.911317.911371.911424.911477.911530.911584.911637 8.16.911690.911743.911797.911850.911903.911956.912009.912063.912116.912169 8.17.912222.912275.912328.912381.912435.912488.912541.912594.912647.912700 8.18.912753.912806.912859.912913.912966.913019.913072.913125.913178.913231 8.19.913284.913337.913390.913443.913496.913549.913602.913655.913708.913761

8.20.913814.913867.913920.913973.914026.914079.914132.914184.914237.914290 8.21.914343.914396.914449.914502.914555.914608.914660.914713.914766.914819 8.22.914872.914925.914977.915030.915083.915136.915189.915241.915294.915347 8.23.915400.915453.915505.915558.915611.915664.915716.915769.915822.915875 8.24.915927.915980.916033.916085.916138.916191.916243.916296.916349.916401 8.25.916454.916507.916559.916612.916664.916717.916770.916822.916875.916927 8.26.916980.917033.917085.917138.917190.917243.917295.917348.917400.917453 8.27.917506.917558.917611.917663.917716.917768.917820.917873.917925.917978 8.28.918030.918083.918135.918188.918240.918293.918345.918397.918450.918502 8.29.918555.918607.918659.918712.918764.918816.918869.918921.918973.919026 8.30.919078.919130.919183.919235.919287.919340.919392.919444.919496.919549 8.31.919601.919653.919706.919758.919810.919862.919914.919967.920019.920071 8.32.920123.920176.920228.920280.920332.920384.920436.920489.920541.920593 8.33.920645.920697.920749.920801.920853.920906.920958.921010.921062.921114 8.34.921166.921218.921270.921322.921374.921426.921478.921530.921582.921634 8.35.921686.921738.921790.921842.921894.921946.921998.922050.922102.922154 8.36.922206.922258.922310.922362.922414.922466.922518.922570.922622.922674 8.37.922725.922777.922829.922881.922933.922985.923037.923089.923140.923192 8.38.923244.923296.923348.923399.923451.923503.923555.923607.923658.923710 8.39.923762.923814.923865.923917.923969.924021.924072.924124.924176.924228

8.40.924279.924331.924383.924434.924486.924538.924589.924641.924693.924744 8.41.924796.924848.924899.924951.925003.925054.925106.925157.925209.925261 8.42.925312.925364.925415.925467.925518.925570.925621.925673.925725.925776 8.43.925828.925879.925931.925982.926034.926085.926137.926188.926240.926291 8.44.926342.926394.926445.926497.926548.926600.926651.926702.926754.926805 8.45.926857.926908.926959.927011.927062.927114.927165.927216.927268.927319 8.46.927370.927422.927473.927524.927576.927627.927678.927730.927781.927832 8.47.927883.927935.927986.928037.928088.928140.928191.928242.928293.928345 8.48.928396.928447.928498.928549.928601.928652.928703.928754.928805.928857 8.49.928908.928959.929010.929061.929112.929163.929215.929266.929317.929368 8.50.929419.929470.929521.929572.929623.929674.929725.929776.929827.929879 8.51.929930.929981.930032.930083.930134.930185.930236.930287.930338.930389 8.52.930440.930491.930542.930592.930643.930694.930745.930796.930847.930898 8.53.930949.931000.931051.931102.931153.931204.931254.931305.931356.931407 8.54.931458.931509.931560.931610.931661.931712.931763.931814.931865.931915 8.55.931966.932017.932068.932118.932169.932220.932271.932322.932372.932423 8.56.932474.932524.932575.932626.932677.932727.932778.932829.932879.932930 8.57.932981.933031.933082.933133.933183.933234.933285.933335.933386.933437 8.58.933487.933538.933589.933639.933690.933740.933791.933841.933892.933943 8.59.933993.934044.934094.934145.934195.934246.934296.934347.934397.934448

8.60.934498.934549.934599.934650.934700.934751.934801.934852.934902.934953 8.61.935003.935054.935104.935154.935205.935255.935306.935356.935406.935457 8.62.935507.935558.935608.935658.935709.935759.935809.935860.935910.935960 8.63.936011.936061.936111.936162.936212.936262.936313.936363.936413.936463 8.64.936514.936564.936614.936665.936715.936765.936815.936865.936916.936966 8.65.937016.937066.937117.937167.937217.937267.937317.937367.937418.937468 8.66.937518.937568.937618.937668.937718.937769.937819.937869.937919.937969 8.67.938019.938069.938119.938169.938219.938269.938320.938370.938420.938470 8.68.938520.938570.938620.938670.938720.938770.938820.938870.938920.938970 8.69.939020.939070.939120.939170.939220.939270.939320.939369.939419.939469 8.70.939519.939569.939619.939669.939719.939769.939819.939869.939918.939968 8.71.940018.940068.940118.940168.940218.940267.940317.940367.940417.940467 8.72.940516.940566.940616.940666.940716.940765.940815.940865.940915.940964 8.73.941014.941064.941114.941163.941213.941263.941313.941362.941412.941462 8.74.941511.941561.941611.941660.941710.941760.941809.941859.941909.941958 8.75.942008.942058.942107.942157.942207.942256.942306.942355.942405.942455 8.76.942504.942554.942603.942653.942702.942752.942801.942851.942901.942950 8.77.943000.943049.943099.943148.943198.943247.943297.943346.943396.943445 8.78.943495.943544.943593.943643.943692.943742.943791.943841.943890.943939 8.79.943989.944038.944088.944137.944186.944236.944285.944335.944384.944433

8.80.944483.944532.944581.944631.944680.944729.944779.944828.944877.944927 8.81.944976.945025.945074.945124.945173.945222.945272.945321.945370.945419 8.82.945469.945518.945567.945616.945665.945715.945764.945813.945862.945912 8.83.945961.946010.946059.946108.946157.946207.946256.946305.946354.946403 8.84.946452.946501.946551.946600.946649.946698.946747.946796.946845.946894 8.85.946943.946992.947041.947090.947140.947189.947238.947287.947336.947385 8.86.947434.947483.947532.947581.947630.947679.947728.947777.947826.947875 8.87.947924.947973.948022.948070.948119.948168.948217.948266.948315.948364

8.88.948413.948462.948511.948560.948609.948657.948706.948755.948804.948853 8.89.948902.948951.948999.949048.949097.949146.949195.949244.949292.949341

8.90.949390.949439.949488.949536.949585.949634.949683.949731.949780.949829 8.91.949878.949926.949975.950024.950073.950121.950170.950219.950267.950316 8.92.950365.950414.950462.950511.950560.950608.950657.950706.950754.950803 8.93.950851.950900.950949.950997.951046.951095.951143.951192.951240.951289 8.94.951338.951386.951435.951483.951532.951580.951629.951677.951726.951775 8.95.951823.951872.951920.951969.952017.952066.952114.952163.952211.952260 8.96.952308.952356.952405.952453.952502.952550.952599.952647.952696.952744 8.97.952792.952841.952889.952938.952986.953034.953083.953131.953180.953228 8.98.953276.953325.953373.953421.953470.953518.953566.953615.953663.953711 8.99.953760.953808.953856.953905.953953.954001.954049.954098.954146.954194

9.00.954243.954291.954339.954387.954435.954484.954532.954580.954628.954677 9.01.954725.954773.954821.954869.954918.954966.955014.955062.955110.955158 9.02.955207.955255.955303.955351.955399.955447.955495.955543.955592.955640 9.03.955688.955736.955784.955832.955880.955928.955976.956024.956072.956120 9.04.956168.956216.956265.956313.956361.956409.956457.956505.956553.956601 9.05.956649.956697.956745.956793.956840.956888.956936.956984.957032.957080 9.06.957128.957176.957224.957272.957320.957368.957416.957464.957512.957559 9.07.957607.957655.957703.957751.957799.957847.957894.957942.957990.958038 9.08.958086.958134.958181.958229.958277.958325.958373.958421.958468.958516 9.09.958564.958612.958659.958707.958755.958803.958850.958898.958946.958994 9.10.959041.959089.959137.959185.959232.959280.959328.959375.959423.959471 9.11.959518.959566.959614.959661.959709.959757.959804.959852.959900.959947 9.12.959995.960042.960090.960138.960185.960233.960280.960328.960376.960423 9.13.960471.960518.960566.960613.960661.960709.960756.960804.960851.960899 9.14.960946.960994.961041.961089.961136.961184.961231.961279.961326.961374 9.15.961421.961469.961516.961563.961611.961658.961706.961753.961801.961848 9.16.961895.961943.961990.962038.962085.962132.962180.962227.962275.962322 9.17.962369.962417.962464.962511.962559.962606.962653.962701.962748.962795 9.18.962843.962890.962937.962985.963032.963079.963126.963174.963221.963268 9.19.963316.963363.963410.963457.963504.963552.963599.963646.963693.963741

9.20.963788.963835.963882.963929.963977.964024.964071.964118.964165.964212 9.21.964260.964307.964354.964401.964448.964495.964542.964590.964637.964684 9.22.964731.964778.964825.964872.964919.964966.965013.965061.965108.965155 9.23.965202.965249.965296.965343.965390.965437.965484.965531.965578.965625 9.24.965672.965719.965766.965813.965860.965907.965954.966001.966048.966095 9.25.966142.966189.966236.966283.966329.966376.966423.966470.966517.966564 9.26.966611.966658.966705.966752.966799.966845.966892.966939.966986.967033 9.27.967080.967127.967173.967220.967267.967314.967361.967408.967454.967501 9.28.967548.967595.967642.967688.967735.967782.967829.967875.967922.967969 9.29.968016.968062.968109.968156.968203.968249.968296.968343.968390.968436 9.30.968483.968530.968576.968623.968670.968716.968763.968810.968856.968903 9.31.968950.968996.969043.969090.969136.969183.969229.969276.969323.969369 9.32.969416.969463.969509.969556.969602.969649.969695.969742.969789.969835 9.33.969882.969928.969975.970021.970068.970114.970161.970207.970254.970300 9.34.970347.970393.970440.970486.970533.970579.970626.970672.970719.970765 9.35.970812.970858.970904.970951.970997.971044.971090.971137.971183.971229 9.36.971276.971322.971369.971415.971461.971508.971554.971601.971647.971693 9.37.971740.971786.971832.971879.971925.971971.972018.972064.972110.972157 9.38.972203.972249.972295.972342.972388.972434.972481.972527.972573.972619 9.39.972666.972712.972758.972804.972851.972897.972943.972989.973035.973082

9.40.973128.973174.973220.973266.973313.973359.973405.973451.973497.973543 9.41.973590.973636.973682.973728.973774.973820.973866.973913.973959.974005 9.42.974051.974097.974143.974189.974235.974281.974327.974374.974420.974466 9.43.974512.974558.974604.974650.974696.974742.974788.974834.974880.974926 9.44.974972.975018.975064.975110.975156.975202.975248.975294.975340.975386 9.45.975432.975478.975524.975570.975616.975662.975707.975753.975799.975845 9.46.975891.975937.975983.976029.976075.976121.976167.976212.976258.976304 9.47.976350.976396.976442.976488.976533.976579.976625.976671.976717.976763 9.48.976808.976854.976900.976946.976992.977037.977083.977129.977175.977220 9.49.977266.977312.977358.977403.977449.977495.977541.977586.977632.977678 9.50.977724.977769.977815.977861.977906.977952.977998.978043.978089.978135 9.51.978181.978226.978272.978317.978363.978409.978454.978500.978546.978591 9.52.978637.978683.978728.978774.978819.978865.978911.978956.979002.979047 9.53.979093.979138.979184.979230.979275.979321.979366.979412.979457.979503 9.54.979548.979594.979639.979685.979730.979776.979821.979867.979912.979958 9.55.980003.980049.980094.980140.980185.980231.980276.980322.980367.980412 9.56.980458.980503.980549.980594.980640.980685.980730.980776.980821.980867 9.57.980912.980957.981003.981048.981093.981139.981184.981229.981275.981320 9.58.981366.981411.981456.981501.981547.981592.981637.981683.981728.981773 9.59.981819.981864.981909.981954.982000.982045.982090.982135.982181.982226

9.60.982271.982316.982362.982407.982452.982497.982543.982588.982633.982678 9.61.982723.982769.982814.982859.982904.982949.982994.983040.983085.983130 9.62.983175.983220.983265.983310.983356.983401.983446.983491.983536.983581 9.63.983626.983671.983716.983762.983807.983852.983897.983942.983987.984032 9.64.984077.984122.984167.984212.984257.984302.984347.984392.984437.984482 9.65.984527.984572.984617.984662.984707.984752.984797.984842.984887.984932 9.66.984977.985022.985067.985112.985157.985202.985247.985292.985337.985382 9.67.985426.985471.985516.985561.985606.985651.985696.985741.985786.985830 9.68.985875.985920.985965.986010.986055.986100.986144.986189.986234.986279 9.69.986324.986369.986413.986458.986503.986548.986593.986637.986682.986727 9.70.986772.986817.986861.986906.986951.986996.987040.987085.987130.987175 9.71.987219.987264.987309.987353.987398.987443.987488.987532.987577.987622 9.72.987666.987711.987756.987800.987845.987890.987934.987979.988024.988068 9.73.988113.988157.988202.988247.988291.988336.988381.988425.988470.988514 9.74.988559.988604.988648.988693.988737.988782.988826.988871.988916.988960 9.75.989005.989049.989094.989138.989183.989227.989272.989316.989361.989405 9.76.989450.989494.989539.989583.989628.989672.989717.989761.989806.989850 9.77.989895.989939.989983.990028.990072.990117.990161.990206.990250.990294 9.78.990339.990383.990428.990472.990516.990561.990605.990650.990694.990738 9.79.990783.990827.990871.990916.990960.991004.991049.991093.991137.991182

9.80.991226.991270.991315.991359.991403.991448.991492.991536.991580.991625 9.81.991669.991713.991758.991802.991846.991890.991935.991979.992023.992067 9.82.992111.992156.992200.992244.992288.992333.992377.992421.992465.992509 9.83.992554.992598.992642.992686.992730.992774.992819.992863.992907.992951 9.84.992995.993039.993083.993127.993172.993216.993260.993304.993348.993392 9.85.993436.993480.993524.993568.993613.993657.993701.993745.993789.993833 9.86.993877.993921.993965.994009.994053.994097.994141.994185.994229.994273 9.87.994317.994361.994405.994449.994493.994537.994581.994625.994669.994713 9.88.994757.994801.994845.994889.994933.994977.995021.995065.995108.995152 9.89.995196.995240.995284.995328.995372.995416.995460.995504.995547.995591 9.90.995635.995679.995723.995767.995811.995854.995898.995942.995986.996030 9.91.996074.996117.996161.996205.996249.996293.996337.996380.996424.996468 9.92.996512.996555.996599.996643.996687.996731.996774.996818.996862.996906 9.93.996949.996993.997037.997080.997124.997168.997212.997255.997299.997343 9.94.997386.997430.997474.997517.997561.997605.997648.997692.997736.997779 9.95.997823.997867.997910.997954.997998.998041.998085.998129.998172.998216 9.96.998259.998303.998347.998390.998434.998477.998521.998564.998608.998652 9.97.998695.998739.998782.998826.998869.998913.998956.999000.999043.999087 9.98.999131.999174.999218.999261.999305.999348.999392.999435.999479.999522

9.99.999565.999609.999652.999696.999739.999783.999826.999870.999913.999957

10.001.000001.000041.000091.000131.000171.000221.000261.000301.000351.00039

对数专题(相关资料及练习)

对数 ●对数 ○对数的发明 16、17世纪之交,随着天文、航海、工程、贸易以及军事的发展,改进数字计算方法成了当务之急。苏格兰数学家纳皮尔(J.Napier,1550—1617)正是在研究天文学的过程中,为了简化其中的计算而发明了对数.对数的发明是数学史上的重大事件,天文学界更是以近乎狂喜的心情迎接这一发明。恩格斯曾经把对数的发明和解析几何的创始、微积分的建立称为17世纪数学的三大成就,伽利略也说过:“给我空间、时间及对数,我就可以创造一个宇宙。” 对数发明之前,人们对三角运算中将三角函数的积化为三角函数的和或差的方法已很熟悉,而且德国数学家斯蒂弗尔(M.Stifel,约1487—1567)在《综合算术》(1544)中阐述的 1,r^2,r^3,r^4, (1) 与 0,1,2,3,… 之间的对应关系(r^n→n)及运算性质(即上面一行数字的乘、除、乘方、开方对应于下面一行数字的加、减、乘、除)也已广为人知。经过对运算体系的多年研究,纳皮尔在1614年出版了《奇妙的对数定律说明书》,书中借助运动学,用几何术语阐述了对数方法。 将对数加以改造使之广泛流传的是纳皮尔的朋友布里格斯(H.Briggs,1561—1631),他通过研究《奇妙的对数定律说明书》,感到其中的对数用起来很不方便,于是与纳皮尔商定,使1的对数为0,10的对数为1,这样就得到了现在所用的以10为底的常用对数。由于我们的数系是十进制,因此它在数值上计算具有优越性。1624年,布里格斯出版了《对数算术》,公布了以10为底包含1~20000及90000~100000的14位常用对数表。 根据对数运算原理,人们还发明了对数计算尺。300多年来,对数计算尺一直是科学工作者,特别是工程技术人员必备的计算工具,直到20世纪70年代才让位给电子计算器。尽管作为一种计算工具,对数计算尺、对数表都不再重要了,但是,对数的思想方法却仍然具有生命力。 从对数的发明过程我们可以发现,纳皮尔在讨论对数概念时,并没有使用指数与对数的互逆关系,造成这种状况的主要原因是当时还没有明确的指数概念,就连指数符号也是在20多年后的1637年才由法国数学家笛卡儿(R.Descartes,1596—1650)开始使用。直到18世纪,才由瑞士数学家欧拉发现了指数与对数的互逆关系。在1770年出版的一部著作中,欧拉首先使用y=a^x来定义x=log (a) y,他指出:“对数源于指数”。对数的发明先于指数,成为数学史上的珍闻。 从对数的发明过程可以看到,社会生产、科学技术的需要是数学发展的主要动力。建立对数与指数之间的联系的过程表明,使用较好的符号体系对于数学的发展是至关重要的。实际上,好的数学符号能够大大地节省人的思维负担。数学家们对数学符号体系的发展与完善作出了长期而艰苦的努力。 ○定义 1.如果 a^x=N(a>0,且a≠1),那么数x叫做以a为底N的对数(logarithm),记作 x=logaN .其中,a叫做对数的底数,N叫做真数。且a>o,a≠1,N>0 2.特别地,我们称以10为底的对数叫做常用对数(common logarithm),并把log10N 记为 lgN.

正态分布z值表

正态分布z值表——见最下文 首先我们得先来了解一下什么是正态分布: 1.正态曲线(normal curve) 正态曲线是簇曲线,呈对称钟形,均数所在处最高,两侧逐渐下降,两端在无穷处与横轴无限接近。横坐标常使用观察值组段,纵坐标常使用频数、频率及概率密度(频率与组距之比)。 2.正态分布特征 曲线概率密度函数: 式中,有4个常数, μ为总体均数,σ为总体标准差,π为圆周率,е为自然对数的底数, 其中μ、σ为不确定的常数,称为正态分布的参数。 μ是位置参数,决定着正态曲线在X轴上的位置; σ是形状参数,决定着正态曲线的分布形状 由此决定的正态分布记作N(μ,σ2)。

仅X 为随机变量。 曲线位置形状与面积特征: 标准差一样规定了曲线的形状相同,而均数不同,会使得曲线在在横轴上的位置不同,并且随着均数增大,曲线逐渐向右移动。

均数不变,标准差改变,标准差小的曲线变异度小,曲线形状就高瘦一点;标准差大的变异度大,曲线形状就矮胖一点。 标准正态分布 均数为0,标准差为1的正态分布被称为标准正态分布(standard normal distribution)。 对于任意一个服从正态分布N(μ,σ2)的随机变量,可做标准化转换。 通过标准化转换后,任意一个正态分布曲线下面积求解问题都能转换成标准正态分布曲线下面积求解问题。如下所示:

2.标准正态分布的应用 当Z的取值范围为(Z1,Z2)时,概率(面积)计算公式应为: P(Z1<Z<Z2)=φ(Z2)﹣φ(Z1) 因为统计表中只有Z值的左侧尾部面积,所以根据上图所示,当Z>0时应有: φ(Z)=1-φ(﹣Z) 所以对于一个一般的正态分布问题,我们可以先通过标准化转换求得Z值,然后查表找到所对应的值后代入面积公式即可进行求解。 注意: ①曲线下面积总和为1。 ②曲线下的面积是从﹣∞积分到当前Z的面积。 ③曲线下对称于0的区间,面积相等。 ④当μ,σ和X已知时,先求Z值,再用Z值查表,得到所求区

自然对数表

自然对数表 1.0 0.0000 0.0100 0.0198 0.0296 0.0392 0.0488 0.0583 0.0677 0.0770 0.0862 1.1 0.0953 0.1044 0.1133 0.1222 0.1310 0.1398 0.1484 0.1570 0.1655 0.1740 1.2 0.1823 0.1906 0.1989 0.2070 0.2151 0.2231 0.2311 0.2390 0.2469 0.2546 1.3 0.2624 0.2700 0.2776 0.2852 0.2927 0.3001 0.3075 0.3148 0.3221 0.3293 1.4 0.3365 0.3436 0.3507 0.3577 0.3646 0.3716 0.3784 0.3853 0.3920 0.3988 1.5 0.4055 0.4121 0.4187 0.4253 0.4318 0.4383 0.4447 0.4511 0.4574 0.4637 1.6 0.4700 0.4762 0.4824 0.4886 0.4947 0.5008 0.5068 0.5128 0.5188 0.5247 1.7 0.5306 0.5365 0.5423 0.5481 0.5539 0.5596 0.5653 0.5710 0.5766 0.5822 1.8 0.5878 0.5933 0.5988 0.6043 0.6098 0.6152 0.6206 0.6259 0.6313 0.6366 1.9 0.6419 0.6471 0.6523 0.6575 0.6627 0.6678 0.6729 0.6780 0.6831 0.6881 2.0 0.6931 0.6981 0.7031 0.7080 0.7129 0.7178 0.7227 0.7275 0.7324 0.7372 2.1 0.7419 0.7467 0.7514 0.7561 0.7608 0.7655 0.7701 0.7747 0.7793 0.7839 2.2 0.7885 0.7930 0.7975 0.8020 0.8065 0.8109 0.8154 0.8198 0.8242 0.8286 2.3 0.8329 0.8372 0.8416 0.8459 0.8502 0.8544 0.8587 0.8629 0.8671 0.8713 2.4 0.8755 0.8796 0.8838 0.8879 0.8920 0.8961 0.9002 0.9042 0.9083 0.9123 2.5 0.9163 0.9203 0.9243 0.9282 0.9322 0.9361 0.9400 0.9439 0.9478 0.9517 2.6 0.9555 0.9594 0.9632 0.9670 0.9708 0.9746 0.9783 0.9821 0.9858 0.9895 2.7 0.9933 0.9969 1.0006 1.0043 1.0080 1.0116 1.0152 1.0188 1.0225 1.0260 2.8 1.0296 1.0332 1.0367 1.0403 1.0438 1.0473 1.0508 1.0543 1.0578 1.0613 2.9 1.0647 1.0682 1.0716 1.0750 1.0784 1.0818 1.0852 1.0886 1.0919 1.0953 3.0 1.0986 1.1019 1.1053 1.1086 1.1119 1.1151 1.1184 1.1217 1.1249 1.1282 3.1 1.1314 1.1346 1.1378 1.1410 1.1442 1.1474 1.1506 1.1537 1.1569 1.1600 3.2 1.1632 1.1663 1.1694 1.1725 1.1756 1.1787 1.1817 1.1848 1.1878 1.1909 3.3 1.1939 1.1969 1.2000 1.2030 1.2060 1.2090 1.2119 1.2149 1.2179 1.2208 3.4 1.2238 1.2267 1.2296 1.2326 1.2355 1.2384 1.2413 1.2442 1.2470 1.2499 3.5 1.2528 1.2556 1.2585 1.2613 1.2641 1.2669 1.2698 1.2726 1.2754 1.2782 3.6 1.2809 1.2837 1.2865 1.2892 1.2920 1.2947 1.2975 1.3002 1.3029 1.3056 3.7 1.3083 1.3110 1.3137 1.3164 1.3191 1.3218 1.3244 1.3271 1.3297 1.3324 3.8 1.3350 1.3376 1.3403 1.3429 1.3455 1.3481 1.3507 1.3533 1.3558 1.3584 3.9 1.3610 1.3635 1.3661 1.3686 1.3712 1.3737 1.3762 1.3788 1.3813 1.3838 4.0 1.3863 1.3888 1.3913 1.3938 1.3962 1.3987 1.4012 1.4036 1.4061 1.4085 4.1 1.4110 1.4134 1.4159 1.4183 1.4207 1.4231 1.4255 1.4279 1.4303 1.4327 4.2 1.4351 1.4375 1.4398 1.4422 1.4446 1.4469 1.4493 1.4516 1.4540 1.4563 4.3 1.4586 1.4609 1.4633 1.4656 1.4679 1.4702 1.4725 1.4748 1.4770 1.4793 4.4 1.4816 1.4839 1.4861 1.4884 1.4907 1.4929 1.4951 1.4974 1.4996 1.5019 4.5 1.5041 1.5063 1.5085 1.5107 1.5129 1.5151 1.5173 1.5195 1.5217 1.5239 4.6 1.5261 1.5282 1.5304 1.5326 1.5347 1.5369 1.5390 1.5412 1.5433 1.5454 4.7 1.5476 1.5497 1.5518 1.5539 1.5560 1.5581 1.5602 1.5623 1.5644 1.5665 4.8 1.5686 1.5707 1.5728 1.5748 1.5769 1.5790 1.5810 1.5831 1.5851 1.5872 4.9 1.5892 1.5913 1.5933 1.5953 1.5974 1.5994 1.6014 1.6034 1.6054 1.6074 5.0 1.6094 1.6114 1.6134 1.6154 1.6174 1.6194 1.6214 1.6233 1.6253 1.6273 5.1 1.6292 1.6312 1.6332 1.6351 1.6371 1.6390 1.6409 1.6429 1.6448 1.6467

对数知识点整理

1对数的概念 如果a(a>0,且a ≠1)的b 次幂等于N ,即N a b =,那么数b 叫做以a 为底N 的对数,记作:b N a =log ,其中a 叫做对数的底数,N 叫做真数. 由定义知: ①负数和零没有对数; ②a>0且a ≠1,N>0; ③01log =a , 1log =a a , b a b a =log ,b a b a =log 特别地,以10为底的对数叫常用对数,记作N 10log ,简记为lgN ;以无理数e(e=2.718 28…) 为底的对数叫做自然对数,记作N e log ,简记为N ln 2对数式与指数式的互化 式子名称指数式N a b =(底数)(指数)(幂值)对数式b N a =log (底数)(对数)(真数) 3对数的运算性质 如果a>0,a ≠1,M>0,N>0,那么 (1)N M MN a a a log log )(log +=(2N M a a log log N)(M log a -=÷(3)M b M a b a log log = 问:①公式中为什么要加条件a>0,a ≠1,M>0,N>0? ②=n a a log ______ (n ∈R) ③对数式与指数式的比较.(学生填表) 运算性质 n m n m a a a +=?,n m n m a a a -=÷ mn n m a a =)((a>0且a ≠1,n ∈R) N M MN a a a log log )(log +=, N M a a log log N)(M log a -=÷(a>0,a ≠1,M>0,N>0) 难点疑点突破 对数定义中,为什么要规定a >0,,且a ≠1? 理由如下: ①若a <0,则N 的某些值不存在,例如log-28 ②若a=0,则N ≠0时b 不存在;N=0时b 不惟一,可以为任何正数 ③若a=1时,则N ≠1时b 不存在;N=1时b 也不惟一,可以为任何正数 为了避免上述各种情况,所以规定对数式的底是一个不等于1的正数

自然对数

自然对数 以常数e为底数的对数叫做自然对数,记作lnN(N>0)。自然对数在物理学、生物学等自然科学中有重要的意义。 1数学表示方法 自然对数的一般表示方法为 数学中也常见以 表示自然对数。若为了避免与基为10的常用对数混淆,可用“全写” 2概念 它的含义是单位时间内,持续的翻倍增长所能达到的极限值 有关概念 自然对数的底数e是由一个重要极限给出的。我们定义:当n趋于无限时, e是一个无限不循环小数,其值约等于2.718281828459…,它是一个超越数。对数函数 当自然对数中真数为连续自变量时,称为对数函数,记作 (x为自变量,y为因变量). e的级数展开式 易证明:函数展开为x的幂级数(Maclaurin级数)是 ; 特别地,当x=1时就得到了e的展开式

3意义 物理学意义 在热力学第二定律中,系统的宏观状态所对应的微观态的多少表现为宏观态的无序程度,同时也决定了宏观过程的方向性。看起来,一个宏观状态对应的微观状态的多少是个很重要的物理量,它标志着这个宏观态的无序程度,从中还可以推知系统将朝什么方向变化。物理学中用字母Ω表示一个宏观状态所对应的微观状态的数目。 为了研究方便,物理学家们用得更多的是一个与Ω相关的物理量,这就是今天常常听到的——熵(entropy),用字母S表示。玻尔兹曼在1877年提出了熵与微观态的数目Ω的关系,即S∝lnΩ,后来普朗克把它写成了等式S=klnΩ,式中k叫做玻尔兹曼常量。如前所述,既然微观态的数目Ω是分子运动无序性的一种量度,由于Ω越大,熵S也越大,那么熵S自然也是系统内分子运动无序性的量度。在引入熵之后,关于自然过程的方向性就可以表述为:在任何自然过程中,一个孤立系统的总熵不会减小。这就是用熵的概念表示的热力学第二定律。为此,不少人也把热力学第二定律叫做熵增加原理。 由熵的定义可以知道,熵较大的宏观状态就是无序程度较大的宏观状态,也就是出现概率较大的宏观状态。在自发过程中熵总是增加的,其原因并非因为有序是不可能的,而是因为通向无序的渠道要比通向有序的渠道多得多。把事情搞得乱糟糟的方式要比把事情做得整整齐齐的方式多得多。要让操场上的一群学生按班级、按身高,或按任何规则来站队都是比较麻烦的:每个学生都要找到自己的位置。但是要让已经站好队的学生解散,那就非常简单:每个学生随便朝一个方向跑去,队形就乱了。从微观的角度看,热力学第二定律是一个统计规律:一个孤立系统总是从熵小的状态向熵大的状态发展,而熵值较大代表着无序,所以自发的宏观过程总是向无序度更大的方向发展。 生物学意义 在连锁交换定律中,重组率或重组值是指双杂合体测交产生的重组型配子的比例,即重组率=重组配字数/总配子数(亲组合+重组和)×100%,重组是交换的结果,所以重组率(recombination fraction)通常也称作交换率(crossing over percentage)或交换值。可是仔细推敲起来,这两个数值是不尽相同。 如果我们假定,沿染色体纵长的各点上交换的发生大体上是随机的。那么可以这样认为,如果两个基因座相距很近,由交换而分开较少,重组率就低;如果两基因座离开很远,交换发生的次数较多,重组率就高。所以可以根据重组率的大小计算有关基因间的相对距离,把基因顺序地排列在染色体上,绘制出基因图。生物学家就是这样做的。 如果有关的两个基因座在染色体上分开较远,举例说重组率在12%-15%以上,那么进行杂交试验时,其间可能发生双交换或四交换等更高数目的偶数交换,形成的配子却仍然是非重组型的。这时如简单地把重组率看作数交换率,那么交换率就要被低估了。因为遗传图是以1%交换率作为图距单位的,所以如交换率低 估了,图距自然也随之缩小了,这就需要校正。校正的公式较多,可根据自己得出的连锁与交换试验的结果,提出单是适用于某一生物的校正公式。一般来说,

常用对数表

708470937101711071187126713571437152 1 0 3 3 4 5 6 7 8 716871777185719372027210721872267235 1 0 2 3 4 5 6 7 7 725172597267727572847292730073087316 1 0 2 3 4 5 6 6 7 733273407348735673647372738073887396 1 0 2 3 4 5 6 6 7 741274197427743574437451745974667474 1 0 2 3 4 5 5 6 7 749074977505751375207528753675437551 1 0 2 3 4 5 5 6 7 756675747582758975977604761276197627 1 0 2 3 4 5 5 6 7 764276497657766476727679768676947701 1 0 2 3 4 4 5 6 7 771677237731773877457752776077677774 1 0 2 3 4 4 5 6 7 778977967803781078187825783278397846 1 0 2 3 4 4 5 6 6 786078687875788278897896790379107917 1 0 2 3 4 4 5 6 6 793179387945795279597966797379807987 1 0 2 3 3 4 5 6 6 800080078014802180288035804180488055 1 0 2 3 3 4 5 5 6 806980758082808980968102810981168122 1 0 2 3 3 4 5 5 6 813681428149815681628169817681828189 1 0 2 3 3 4 5 5 6 820282098215822282288235824182488254 1 0 2 3 3 4 5 5 6 826782748280828782938299830683128319 1 0 2 3 3 4 5 5 6 833183388344835183578363837083768382 1 0 2 3 3 4 4 5 6 839584018407841484208426843284398445 1 0 2 2 3 4 4 5 6 845784638470847684828488849485008506 1 0 2 2 3 4 4 5 6 851985258531853785438549855585618567 1 0 2 2 3 4 4 5 5 857985858591859786038609861586218627 1 0 2 2 3 4 4 5 5 863986458651865786638669867586818686 1 0 2 2 3 4 4 5 5 869887048710871687228727873387398745 1 0 2 2 3 3 4 5 5 875687628768877487798785879187978802 1 0 2 2 3 3 4 5 5 881488208825883188378842884888548859 1 0 2 2 3 3 4 5 5 887188768882888788938899890489108915 1 0 2 2 3 3 4 4 5 892789328938894389498954896089658971 1 0 2 2 3 3 4 4 5 898289878993899890049009901590209025 1 0 2 2 3 3 4 4 5 903690429047905390589063906990749079 1 0 2 2 3 3 4 4 5 909090969101910691129117912291289133 1 0 2 2 3 3 4 4 5 914391499154915991659170917591809186 1 0 2 2 3 3 4 4 5 919692019206921292179222922792329238 1 0 2 2 3 3 4 4 5 924892539258926392699274927992849289 1 0 2 2 3 3 4 4 5 929993049309931593209325933093359340 1 0 2 2 3 3 4 4 5 935093559360936593709375938093859390 1 0 2 2 3 3 4 4 5 9400940594109415942094259430943594400 0 1 2 2 3 3 4 4 9450945594609465946994749479948494890 0 1 2 2 3 3 4 4 9499950495099513951895239528953395380 0 1 2 2 3 3 4 4 9547955295579562956695719576958195860 0 1 2 2 3 3 4 4 9595960096059609961496199624962896330 0 1 2 2 3 3 4 4

1-10000常用对数表

1 0 2 0.301029996 3 0.477121255 4 0.602059991 5 0.698970004 6 0.77815125 7 0.84509804 8 0.903089987 9 0.954242509 10 1 11 1.041392685 12 1.079181246 13 1.113943352 14 1.146128036 15 1.176091259 16 1.204119983 17 1.230448921 18 1.255272505 19 1.278753601 20 1.301029996 21 1.322219295 22 1.342422681 23 1.361727836 24 1.380211242 25 1.397940009 26 1.414973348 27 1.431363764 28 1.447158031 29 1.462397998 30 1.477121255 31 1.491361694 32 1.505149978 33 1.51851394 34 1.531478917 35 1.544068044 36 1.556302501 37 1.568201724 38 1.579783597 39 1.591064607 40 1.602059991 41 1.612783857 42 1.62324929 43 1.633468456 44 1.643452676

45 1.653212514 46 1.662757832 47 1.672097858 48 1.681241237 49 1.69019608 50 1.698970004 51 1.707570176 52 1.716003344 53 1.72427587 54 1.73239376 55 1.740362689 56 1.748188027 57 1.755874856 58 1.763427994 59 1.770852012 60 1.77815125 61 1.785329835 62 1.792391689 63 1.799340549 64 1.806179974 65 1.812913357 66 1.819543936 67 1.826074803 68 1.832508913 69 1.838849091 70 1.84509804 71 1.851258349 72 1.857332496 73 1.86332286 74 1.86923172 75 1.875061263 76 1.880813592 77 1.886490725 78 1.892094603 79 1.897627091 80 1.903089987 81 1.908485019 82 1.913813852 83 1.919078092 84 1.924279286 85 1.929418926 86 1.934498451 87 1.939519253 88 1.944482672

对数公式

对数 目录 对数的概念 定义 若a^n=b(a>0且a≠1) 则n=log(a)(b) 基本性质 如果a>0,且a≠1,M>0,N>0,那么:

1、a^log(a)(b)=b 2、log(a)(a)=1 3、log(a)(MN)=log(a)(M)+log(a)(N); 4、log(a)(M÷N)=log(a)(M)-log(a)(N); 第5条的公式写法 5、log(a)(M^n)=nlog(a)(M) 6、log(a)[M^(1/n)]=log(a)(M)/n (注:下文^均为上标符号,例:a^1即为a) 推导 1、因为n=log(a)(b),代入则a^n=b,即a^(log(a)(b))=b。 2、因为a^b=a^b 令t=a^b 所以a^b=t,b=log(a)(t)=log(a)(a^b) 令b=1,则1=log(a)(a) 3、MN=M×N 由基本性质1(换掉M和N) a^[log(a)(MN)] = a^[log(a)(M)]×a^[log(a)(N)] =(M)*(N) 由指数的性质 a^[log(a)(MN)] = a^{[log(a)(M)] + [log(a)(N)]} 两种方法只是性质不同,采用方法依实际情况而定 又因为指数函数是单调函数,所以 log(a)(MN) = log(a)(M) + log(a)(N) 4、与(3)类似处理 M/N=M÷N 由基本性质1(换掉M和N) a^[log(a)(M÷N)] = a^[log(a)(M)]÷a^[log(a)(N)] 由指数的性质 a^[log(a)(M÷N)] = a^{[log(a)(M)] - [log(a)(N)]} 又因为指数函数是单调函数,所以 log(a)(M÷N) = log(a)(M) - log(a)(N) 5、与(3)类似处理 M^n=M^n 由基本性质1(换掉M) a^[log(a)(M^n)] = {a^[log(a)(M)]}^n 由指数的性质

对数+常用公式方便搜到的人

对数 来自维基百科 各种底数的对数: 红色函数底数是e, 绿色函数底数是10,而紫色函数底数是1.7。在数轴上每个刻度是一个单位。所有底数的对数函数都通过点(1,0),因为任何数的0次幂都是1,而底数β的函数通过点(β, 1),因为任何数的1次幂都是自身1。曲线接近y轴但永不触及它,因为x=0的奇异性。 在数学中,数?x(对于底数?β)的对数是βy?的指数?y,使得?x=βy。底数?β?的值一定不能是1或0(在扩展到复数的复对数情况下不能是1的方根),典型的是e、?10或2。数x(对于底数β)的对数通常写为

。 当x和β进一步限制为正实数的时候,对数是1个唯一的实数。例如,因为 , 我们可以得出 , 用日常语言说,对81以3为基的对数是4。 对数函数 函数log αx依赖于α和x二者,但是术语对数函数在标准用法中用来称呼形如log αx的函数,在其中底数α是固定的而只有一个参数x。所 以对每个基的值(不得是负数、0或1)只有唯一的对数函数。从这个角度看,底数α的对数函数是指数函数y= αx的反函数。词语“对数”经常用来称呼对数函数自身和这个函数的1个特定值。 对数函数图像和指数函数图像关于直线y=x对称,互为逆函数。 对数函数的性质有:

1.都过(1,0)点; 2.定义域为|R|≠0,值域为R; 3.α>1,在(0,+∞)上是增函数;1>α>0时,在(0,+∞)上是减函数。常用公式 ?和差 ?基变换

?指系 ?还原 ?互换 ?倒数

链式 有理和无理指数 如果n是有理数,βn表示等于β的n个因子的乘积: 。 但是,如果β是不等于1的正实数,这个定义可以扩展到在一个域中的任何实数n(参见幂)。类似的,对数函数可以定义于任何正实数。对于不等于1的每个正底数β,有一个对数函数和一个指数函数,它们互为反函数。

常用相对数

常用相对数 相对数是两个有联系的指标的比 1、率(频率指标):说明某种现象发生的频率(频繁程度)或强度。常已百分率(%)、千分(‰)、万分率(1/万)、十万分率(1/10万)等表示。 率= 某现象发生数×100%(或1000 ‰) 可能发生某现象的总数 2、构成比(构成指标)说明某事物内部各构成部分所占的比重分布,常以百分比(%)表示。其计算公式为: 构成比= 某一构成部分的个体数×100% 事物各构成部分个体数的总和 注意 (1)计算相对数的分母一般不宜过小; (2)构成比正常可能说明比重或分布,不能说明发生的频率或强度; (3)在一定的条件下,构成比也可反应率的变化趋势; (4)计算几个率的平均率时,不能直接将几个率相加求其平均率; (5)要在相同条件下进行率和构成比的对比。 ※发病率※罹患率※感染率※死亡率※病死率 三间分布 人群分布 时间分布 地区分布 统计表与统计图 统计表与统计图是表达统计数量关系的重要工具。 统计表是用表格形式,把事物之间的数量关系表示出来。 统计图是用点、线、面的形式,把事物之间的数量关系表示出来。 统计表:原则是简单明了。 1、标题 2、标目(纵标目、横标目) 3、线条 4、数字 5、备注。 统计图 统计图有多种,卫生统计统计学中常用的有直条图、构成图、线图、直方图和统计地图。 制图的基本要求是: 1、根据资料的性质分析目的,正确选择适合的图形; 2、要有标题,扼要地说明资料的内容,必要时注明时间、地点,一般写在图的下面。 3、直条图、线图和直方图都有纵轴和横轴。横轴尺度自左而右,纵轴尺度自上而下,数量一律由小到大,并需用等距标明。直条图和直方图纵坐标从0开始,要标明0点,纵横轴应用标目,注明单位。 统计图(续) 4、比较不同事物时,用不同的线条或颜色表示,要附有图例说明。 直条图:用相同宽度的直条长短来表示各相互独立的指标的数值大小。 构成图:用于表示全体中各部分的比重。 线图:用于表示某现象数量随另一现象而变动的趋势。 直方图:用于表示变量的频繁分布。

e是自然对数的底数

ln和e是什么关系? 对数和底数是干嘛的? 三角函数的画图? ln就是loge lne=logee=1 lne=1 他俩没啥关系一个是运算符号一个是自然数e的ln次方等于1 e^(ln3)=3 In=loge ln(1)=loge(1)=0 e=2.71多 e是自然对数的底数,是一个无限不循环小数。e在科学技术中用得非常多,一般不使用以10为底数的对数。学习了高等数学后就会知道,许多结果和它有紧密的联系,以e为底数,许多式子都是最简的,用它是最“自然”的,所以叫“自然对数”,因而在涉及对数运算的计算中一般使用它,是一个数学符号,没有很具体的意义。其值是2.71828……,是这样定义的: 当n->∞时,(1+1/n)^n的极限。 注:x^y表示x的y次方。 你看,随着n的增大,底数越来越接近1,而指数趋向无穷大,那结果到底是趋向于1还是无穷大呢?其实,是趋向于2.718281828……这个无限不循环小数1+1/1!+1/2!+1 /3!+1/4!+……+1/n!,当n趋近无穷时,其极限值就为e. 对数(Logarithm 若)。则b叫做以a为底N的对数,记作。当a=10时称作常用对数,当a=e时,称作自然对数。 我们知道,一般对数的底可以为任意不等于1的正数。即对数的底如果为超越数e(e=2.718)我们就把这样的对数叫作自然对数,用符号“LN”表示。在这里“1”是对数“logarithm"的第一个字母,“N”是自然“nature"的第一个字母,把两个字母合在一起,就表示自然对数。 “lg”才表示以10为底的对数!!!! ln1=0 表示e的0次方=1 ln100=4.605170…… 表示e的4.605170次方=100

对数公式总结

1对数的概念 如果a(a>0,且a≠1)的b次幂等于N,即ab=N,那么数b叫做以a为底N的对数,记作:logaN=b,其中a叫做对数的底数,N叫做真数. 由定义知: ①负数和零没有对数; ②a>0且a≠1,N>0; ③loga1=0,logaa=1,alogaN=N,logaab=b. 特别地,以10为底的对数叫常用对数,记作log10N,简记为lgN;以无理数e(e=2.718 28…)为底的对数叫做自然对数,记作logeN,简记为lnN. 2对数式与指数式的互化 式子名称abN指数式ab=N(底数)(指数)(幂值)对数式logaN=b(底数)(对数)(真数) 3对数的运算性质 如果a>0,a≠1,M>0,N>0,那么 (1)loga(MN)=logaM+logaN. (2)logaMN=logaM-logaN. (3)logaMn=nlogaM (n∈R). 问:①公式中为什么要加条件a>0,a≠1,M>0,N>0? ②logaan=? (n∈R) ③对数式与指数式的比较.(学生填表) 式子ab=NlogaN=b名称a—幂的底数 b— N—a—对数的底数 b— N—运 算 性 质am?an=am+n am÷an= (am)n= (a>0且a≠1,n∈R)logaMN=logaM+logaN logaMN= logaMn=(n∈R) (a>0,a≠1,M>0,N>0) 难点疑点突破 对数定义中,为什么要规定a>0,,且a≠1? 理由如下: ①若a<0,则N的某些值不存在,例如log-28 ②若a=0,则N≠0时b不存在;N=0时b不惟一,可以为任何正数 ③若a=1时,则N≠1时b不存在;N=1时b也不惟一,可以为任何正数 为了避免上述各种情况,所以规定对数式的底是一个不等于1的正数 解题方法技巧 1

对数公式及对数函数的总结

对数运算和对数函数 对数的定义 ①若(0,1)x a N a a =>≠且,则x 叫做以a 为底N 的对数,记作log a x N =,其中a 叫做底数,N 叫做真数. ②负数和零没有对数。③对数式与指数式的互化:log (0,1,0)x a x N a N a a N =?=>≠>。 常用对数与自然对数 常用对数:lg N ,即10log N ;自然对数:ln N ,即log e N (其中 2.71828e =…). 对数函数及其性质

类型一、对数公式的应用 1计算下列对数 =-3log 6log 22 =?3 1log 12 log 2 22 2 =+2lg 5lg =61000lg =+64log 128log 22 =?)24(log 432 =++)2log 2)(log 3log 3(log 9384 =++3log 23log 2242 =?16log 27log 32 =+-2log 90log 5log 333 =++c b a 842log log log =+++200 199lg 43lg 32lg =++32log 8log 8log 842 =+25.0log 10log 255 =-64log 325log 225 =)))65536(log (log (log log 2222 2 解对数的值: 18lg 7lg 37lg 214lg -+- 0 =-+-1)21 (2lg 225lg -1 1 3 341log 2log 8?? -? ??? 的值0 提示:对数公式的运算 如果0,1,0,0a a M N >≠>>,那么 (1)加法:log log log ()a a a M N MN += (2)减法:log log log a a a M M N N -= (3)数乘:log log ()n a a n M M n R =∈ (4)log a N a N = (5)log log (0,)b n a a n M M b n R b =≠∈ (6)换底公式:log log (0,1)log b a b N N b b a = >≠且 (7)1log log =?a b b a (8)a b b a log 1log = 类型二、求下列函数的定义域问题 1函数)13lg(13)(2 ++-= x x x x f 的定义域是)1,31 (- 2设()x x x f -+=22lg ,则?? ? ??+??? ??x f x f 22的定义域为 ()()4,11,4 -- 3 函数()f x =的定义域为( ]1,0()0,1( - ) 提示:(1)分式函数,分母不为0,如0,1 ≠= x x y 。

自然对数表

自然对数表 N 0 1 2 3 4 5 6 7 8 9 1.0 0.0000 0.0100 0.0198 0.0296 0.0392 0.0488 0.0583 0.0677 0.0770 0.0862 1.1 0.0953 0.1044 0.1133 0.1222 0.1310 0.1398 0.1484 0.1570 0.1655 0.1740 1.2 0.1823 0.1906 0.1989 0.2070 0.2151 0.2231 0.2311 0.2390 0.2469 0.2546 1.3 0.2624 0.2700 0.2776 0.2852 0.2927 0.3001 0.3075 0.3148 0.3221 0.3293 1.4 0.3365 0.3436 0.3507 0.3577 0.3646 0.3716 0.3784 0.3853 0.3920 0.3988 1.5 0.4055 0.4121 0.4187 0.4253 0.4318 0.4383 0.4447 0.4511 0.4574 0.4637 1.6 0.4700 0.4762 0.4824 0.4886 0.4947 0.5008 0.5068 0.5128 0.5188 0.5247 1.7 0.5306 0.5365 0.5423 0.5481 0.5539 0.5596 0.5653 0.5710 0.5766 0.5822 1.8 0.5878 0.5933 0.5988 0.6043 0.6098 0.6152 0.6206 0.6259 0.6313 0.6366 1.9 0.6419 0.6471 0.6523 0.6575 0.6627 0.6678 0.6729 0.6780 0.6831 0.6881 2.0 0.6931 0.6981 0.7031 0.7080 0.7129 0.7178 0.7227 0.7275 0.7324 0.7372 2.1 0.7419 0.7467 0.7514 0.7561 0.7608 0.7655 0.7701 0.7747 0.7793 0.7839 2.2 0.7885 0.7930 0.7975 0.8020 0.8065 0.8109 0.8154 0.8198 0.8242 0.8286 2.3 0.8329 0.8372 0.8416 0.8459 0.8502 0.8544 0.8587 0.8629 0.8671 0.8713 2.4 0.8755 0.8796 0.8838 0.8879 0.8920 0.8961 0.9002 0.9042 0.9083 0.9123 2.5 0.9163 0.9203 0.9243 0.9282 0.9322 0.9361 0.9400 0.9439 0.9478 0.9517 2.6 0.9555 0.9594 0.9632 0.9670 0.9708 0.9746 0.9783 0.9821 0.9858 0.9895 2.7 0.9933 0.9969 1.0006 1.0043 1.0080 1.0116 1.0152 1.0188 1.0225 1.0260 2.8 1.0296 1.0332 1.0367 1.0403 1.0438 1.0473 1.0508 1.0543 1.0578 1.0613 2.9 1.0647 1.0682 1.0716 1.0750 1.0784 1.0818 1.0852 1.0886 1.0919 1.0953 3.0 1.0986 1.1019 1.1053 1.1086 1.1119 1.1151 1.1184 1.1217 1.1249 1.1282 3.1 1.1314 1.1346 1.1378 1.1410 1.1442 1.1474 1.1506 1.1537 1.1569 1.1600

高中数学拓展知识-对数表

对数表的历史 对数表的应用领域是极其广阔的,但对数表的编制也经历了一个漫长的过程。 早在公元前200年,古希腊数学家阿基米德(Archimedes )就注意到表2-2中两数列之间的关系: 100 101 102 103 104 105 106 107 0 1 2 3 4 5 6 7 … 可以用下面数列中两数的加、减关系来替代上面数列中两数的乘、除关系,这样就把繁复的乘、除运算转化成简单的加、减运算。 在1544年,德国数学家施蒂费尔(Stifel ,1487-1567)在《整数的算术》中又重新发现了这个性质。 不过,Archimedes 和Stifel 的先驱性工作,成了Napier 发明对数的“巨人肩膀”。 在1594年,Napier 发明了对数,在1614年出版的《奇妙的对数定律说明书》中公布了他编制的间隔为1′的7位正弦对数表。 要编制对数表,先要解决选择底数的问题。我们已经学过换底公式 a b b c c a log log log , 所以,只要选择合适的底数使对数表编制方便就可以了。 如果以a =10为底数,则有 表2-2 表2-3

b a log 0.0000 0.0001 0.0002 0.0003 ?? b 1.0000 ?? 显然,这种对数表的真数多是无理数,使用起来很不方便。 如果以a =1010000为底数,则有 b a log 0.0000 0.0001 0.0002 0.0003 ?? b 1.0000 101 102 103 ?? 显然,这种对数表的真数间隔很大,使用起来也不方便。 如果以a =1.000110000为底数,则有 b a log 0.0000 0.0001 0.0002 0.0003 ?? b 1.0000 1.000100 1.000200 1.000300 ?? 显然,这种对数表的真数间隔已经小多了。 实际上,要使间隔更小,可以取底数1(1+) n a n =,其中n>10000。 Napier 编制第一张对数表时选1000000)0000001.1(=a 。 纳皮尔的对数发表后,就得到英国数学家布里格斯(Briggs )的充分肯定和积极响应。他建议纳皮尔选用10来作为对数的底,因为这有利于对十进位的数取对数。 纳皮尔很赞成布里格斯的意见,然而他已有点力不从心了。制造对数表的任务后来便落在布里格斯及荷兰青年弗拉格(Vlacq )身上。他们终于完成了从1到100000,精确到14位的常用对数表。 表2-4 表2-5

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