روش استفاده:
- اگر میخواهید لوگاریتم طبیعی عدد 2.85 را بیابی؛
- سطر با N=2.8 را بیابید؛
- ستون 5 را بیابید، عدد در سطر 2.8 و ستون 5 این عدد خواهد بود: 1.04732
- پس نتیجه یعنی لوگاریتم طبیعی عدد 2.85 این میباشد: 1.04732
| N | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|---|---|---|---|
| 1.0 | 0 | 3z99503 | .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 |
| N | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| 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 |
| N | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| 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 |
| N | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| 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 |
| N | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| 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 |
| N | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| 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 |
| N | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| 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 |
| N | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| 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 |
| N | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| 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 |
| 10.0 | 2.30259 | 2.30358 | 2.30458 | 2.30558 | 2.30658 | 2.30757 | 2.30857 | 2.30956 | 2.31055 | 2.31154 |
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