Sponsored by the Institute of Physics   Numbers   Addition Table   Multiplication Table   Roman Numerals   Metric Prefixes   Base-n Conversions   Log Table Algebra Trigonometry Calculus Matrices Limits Complex Numbers SI Units Symbols   Printer Version Maths Numbers - Log Table How to find the logarithm of a number, using four figure log tables (below) To find the log of a number, you first need the two parts of the answer - the index or characteristic (the part before the decimal point) and the mantissa (the decimal part after the decimal point). For example, the index of 2.6742 is 2 and the mantissa is .6742.   Finding the index of a logarithm This is easy if you follow these rules: For numbers with more than 1 digit before the decimal point (10 and above), the index will always be one less than the number of digits before the decimal point. For example, the index of 245.211 is 2, the index of 24521.1 is 4 and the index of 24.5211 is 1. For numbers with just 1 digit before the decimal point (1 to 9), the index will be 0. For numbers less than 1, then index will be one more than the number of zeros between the decimal point and the first significant figure. For example, the index of 0.245211 is (bar) 1, the index of 0.00245211 is (bar) 3 and the index of 0.000245211 is (bar) 4.   Finding the mantissa of a logarithm Use the numbers at the far left of the table to give the first two significant figures of the number. If there are more than two digits in the number, follow across the table - the column headings give the third digit of the number. The numbers given in the log table represent the mantissa part of the answer. For Example: To find log 45, follow down the numbers on the far left of the table until you reach 45. The number in the column headed 0 will be the mantissa - the index is 1 (see above) - so log 45 = 1.6532. To find log 456, follow down the numbers on the far left of the table until you reach 45 and take the number in column 6. The index is 2, so log 456 = 2.6590.   Using the Mean Difference Column for numbers with four digits For numbers with four digits, simply add the number in the mean difference column (right hand 9 columns) to the answer you would get if you just ignored the fourth digit. For Example: To find log 4567, take the log of 456 (2.6590) and add the number in column 7 of the mean differences (7) to the mantissa. ie. log 4567 = 3.6590 + 0.0007 = 3.6597.   Finding logs of numbers smaller than one This is simple - just find the log of the four significant figures of the number, and and take away the index. For Example: To find the log of 0.004567, take log 4.567 = 0.6597 and subtract 3 (the index). So log 0.004567 = (log 4.567) - 3 = -2.3403.   N 0 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 10 0000 0043 0086 0128 0170 5 9 13 17 21 26 30 34 38 0212 0253 0294 0334 0374 4 8 12 16 20 24 28 32 36 11 0414 0453 0492 0531 0569 4 8 12 16 20 23 27 31 35 0607 0645 0682 0719 0755 4 7 11 15 18 22 26 29 33 12 0792 0828 0864 0899 0934 3 7 11 14 18 21 25 28 32 0969 1004 1038 1072 1106 3 7 10 14 17 20 24 27 31 13 1139 1173 1206 1239 1271 3 6 10 13 16 19 23 26 29 1303 1335 1367 1399 1430 3 7 10 13 16 19 22 25 29 14 1461 1492 1523 1553 1584 3 6 9 12 15 19 22 25 28 1614 1644 1673 1703 1732 3 6 9 12 14 17 20 23 26 15 1761 1790 1818 1847 1875 3 6 9 11 14 17 20 23 26 1903 1931 1959 1987 2014 3 6 8 11 14 17 19 22 25 16 2041 2068 2095 2122 2148 3 6 8 11 14 16 19 22 24 2175 2201 2227 2253 2279 3 5 8 10 13 16 18 21 23 17 2304 2330 2355 2380 2405 3 5 8 10 13 15 18 20 23 2430 2455 2480 2504 2529 3 5 8 10 12 15 17 20 22 18 2553 2577 2601 2625 2648 2 5 7 9 12 14 17 19 21 2672 2695 2718 2742 2765 2 4 7 9 11 14 16 18 21 19 2788 2810 2833 2856 2878 2 4 7 9 11 13 16 18 20 2900 2923 2945 2967 2989 2 4 6 8 11 13 15 17 19 N 0 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 20 3010 3032 3054 3075 3096 3118 3139 3160 3181 3201 2 4 6 8 11 13 15 17 19 21 3222 3243 3263 3284 3304 3324 3345 3365 3385 3404 2 4 6 8 10 12 14 16 18 22 3424 3444 3464 3483 3502 3522 3541 3560 3579 3598 2 4 6 8 10 12 14 15 17 23 3617 3636 3655 3674 3692 3711 3729 3747 3766 3784 2 4 6 7 9 11 13 15 17 24 3802 3820 3838 3856 3874 3892 3909 3927 3945 3962 2 4 5 7 9 11 12 14 16 25 3979 3997 4014 4031 4048 4065 4082 4099 4116 4133 2 3 5 7 9 10 12 14 15 26 4150 4166 4183 4200 4216 4232 4249 4265 4281 4298 2 3 5 7 8 10 11 13 15 27 4314 4330 4346 4362 4378 4393 4409 4425 4440 4456 2 3 5 6 8 9 11 13 14 28 4472 4487 4502 4518 4533 4548 4564 4579 4594 4609 2 3 5 6 8 9 11 12 14 29 4624 4639 4654 4669 4683 4698 4713 4728 4742 4757 1 3 4 6 7 9 10 12 13 N 0 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 30 4771 4786 4800 4814 4829 4843 4857 4871 4886 4900 1 3 4 6 7 9 10 11 13 31 4914 4928 4924 4955 4969 4983 4997 5011 5024 5038 1 3 4 6 7 8 10 11 12 32 5051 5065 5079 5092 5105 5119 5132 5145 5159 5172 1 3 4 5 7 8 9 11 12 33 5185 5198 5211 5224 5237 5250 5263 5276 5289 5302 1 3 4 5 6 8 9 10 12 34 5315 5328 5340 5353 5366 5378 5391 5403 5416 5428 1 3 4 5 6 8 9 10 11 35 5441 5453 5465 5478 5490 5502 5514 5527 5539 5551 1 2 4 5 6 7 9 10 11 36 5563 5575 5587 5599 5611 5623 5635 5647 5658 5670 1 2 4 5 6 7 8 10 11 37 5682 5694 5705 5717 5729 5740 5752 5763 5775 5786 1 2 3 5 6 7 8 9 10 38 5798 5809 5821 5823 5843 5855 5866 5877 5888 5899 1 2 3 5 6 7 8 9 10 39 5911 5922 5933 5944 5955 5966 5977 5988 5999 6010 1 2 3 5 6 7 8 9 10 N 0 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 40 6021 6031 6042 6053 6064 6075 6085 6069 6107 6117 1 2 3 4 5 6 8 9 10 41 6128 6138 6149 6160 6170 6180 6191 6201 6212 6222 1 2 3 4 5 6 7 8 9 42 6232 6243 6253 6263 6274 6284 6294 6304 6314 6235 1 2 3 4 5 6 7 8 9 43 6335 6345 6355 6365 6375 6385 6395 6405 6415 6425 1 2 3 4 5 6 7 8 9 44 6435 6444 6454 6464 6474 6484 6493 6503 6513 6522 1 2 3 4 5 6 7 8 9 45 6532 6542 6551 6561 6571 6580 6590 6599 6609 6618 1 2 3 4 5 6 7 8 9 46 6628 6637 6646 6656 6665 6675 6684 6693 6702 6712 1 2 3 4 5 6 7 7 8 47 6721 6730 6739 6749 6758 6767 6776 6785 6794 6803 1 2 3 4 5 5 6 7 8 48 6812 6821 6830 6839 6848 6857 6866 6875 6884 6893 1 2 3 4 4 5 6 7 8 49 6902 6911 6920 6928 6937 6946 6955 6904 6972 6981 1 2 3 4 4 5 6 7 8 N 0 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 50 6990 6998 7007 7016 7024 7033 7042 7050 7059 7067 1 2 3 4 5 6 7 8 51 7076 7084 7093 7101 7110 7118 7126 7135 7143 7152 1 2 3 4 5 6 7 8 52 7160 7168 7177 7185 7193 7202 7210 7218 7226 7235 1 2 2 4 5 6 7 7 53 7243 7251 7259 7267 7275 7284 7292 7300 7308 7316 1 2 2 4 5 6 6 7 54 7324 7332 7340 7348 7356 7364 7372 7380 7388 7396 1 2 2 4 5 6 6 7 55 7404 7412 7419 7427 7435 7443 7451 7459 7466 7474 1 2 2 3 4 5 5 6 7 56 7482 7490 7497 7505 7513 7520 7528 7536 7545 7551 1 2 2 3 4 5 5 6 7 57 7559 7566 7574 7582 7589 7597 7604 7612 7619 7627 1 2 2 3 4 5 5 6 7 58 7634 7642 7649 7657 7664 7672 7679 7686 7694 7701 1 1 2 3 4 4 5 6 7 59 7709 7716 7723 7731 7738 7745 7752 7760 7767 7774 1 1 2 3 4 4 5 6 7 N 0 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 60 7782 7789 7796 7803 7810 7818 7825 7832 7839 7846 1 1 2 3 4 4 5 6 6 61 7853 7860 7868 7875 7882 7889 7896 7903 7910 7917 1 1 2 3 4 4 5 6 6 62 7924 7931 7938 7945 7952 7959 7966 7973 7980 7987 1 1 2 3 3 4 5 6 6 63 7993 8000 8007 8014 8021 8028 8035 8041 8048 8055 1 1 2 3 3 4 5 5 6 64 8062 8069 8075 8082 8089 8096 8102 8109 8116 8122 1 1 2 3 3 4 5 5 6 65 8129 8136 8142 8149 8156 8162 8169 8176 8182 8189 1 1 2 3 3 4 5 5 6 66 8195 8202 8209 8215 8222 8228 8235 8241 8248 8254 1 1 2 3 3 4 5 5 6 67 8261 8267 8274 8280 8287 8293 8299 8306 8312 8319 1 1 2 3 3 4 5 5 6 68 8325 8331 8338 8344 8351 8357 8363 8370 8376 8382 1 1 2 3 3 4 4 5 6 69 8388 8395 8401 8407 8414 8420 8426 8432 8439 8445 1 1 2 2 3 4 4 5 6 N 0 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 70 8451 8457 8463 8470 8476 8482 8488 8494 8500 8506 1 1 2 2 3 4 4 5 6 71 8513 8519 8525 8531 8537 8543 8549 8555 8561 8567 1 1 2 2 3 4 4 5 5 72 8573 8579 8585 8591 8597 8603 8609 8615 8621 8627 1 1 2 2 3 4 4 5 5 73 8633 8639 8645 8651 8657 8663 8669 8675 8681 8686 1 1 2 2 3 4 4 5 5 74 8692 8698 9704 8710 8716 8722 8727 8733 8739 8745 1 1 2 2 3 4 4 5 5 75 8751 8756 8762 8768 8774 8779 8785 8791 8797 8802 1 1 2 2 3 3 4 5 5 76 8808 8814 8820 8825 8831 8837 8842 8848 8854 8859 1 1 2 2 3 3 4 5 5 77 8865 8871 8876 8882 8887 8893 8899 8904 8910 8915 1 1 2 2 3 3 4 4 5 78 8921 8927 8932 8938 8943 8949 8954 8960 8965 8971 1 1 2 2 3 3 4 4 5 79 8976 8982 8987 8993 8998 9004 9009 9015 9020 9025 1 1 2 2 3 3 4 4 5 N 0 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 80 9031 9036 9042 9047 9053 9058 9063 9069 9074 9079 1 1 2 2 3 3 4 4 5 81 9085 9090 9096 9101 9106 9112 9117 9122 9128 9133 1 1 2 2 3 3 4 4 5 82 9138 9143 9149 9154 9159 9165 9170 9175 9180 9186 1 1 2 2 3 3 4 4 5 83 9191 9196 9201 9206 9212 9217 9222 9227 9232 9238 1 1 2 2 3 3 4 4 5 84 9243 9248 9253 9258 9263 9269 9274 9279 9284 9289 1 1 2 2 3 3 4 4 5 85 9249 9299 9304 9309 9315 9320 9325 9330 9335 9340 1 1 2 2 3 3 4 4 5 86 9345 9350 9355 9360 9365 9370 9375 9380 9385 9390 1 1 2 2 3 3 4 4 5 87 9395 9400 9405 9410 9415 9420 9425 9430 9435 9440 0 1 1 2 2 3 3 4 4 88 9445 9450 9455 9460 9465 9469 9474 9479 9484 9489 0 1 1 2 2 3 3 4 4 89 9494 9499 9504 9509 9513 9518 9523 9528 9533 9538 0 1 1 2 2 3 3 4 4 N 0 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 90 9542 9547 9552 9557 9562 9566 9571 9576 9581 9586 0 1 1 2 2 3 3 4 4 91 9590 9595 9600 9605 9609 9614 9619 9624 9628 9633 0 1 1 2 2 3 3 4 4 92 9638 9643 9647 9652 9657 9661 9666 9671 9675 9680 0 1 1 2 2 3 3 4 4 93 9685 9689 9694 9699 9703 9708 9713 9717 9722 9727 0 1 1 2 2 3 3 4 4 94 9731 9736 9741 9743 9750 9754 9759 9763 9768 9773 0 1 1 2 2 3 3 4 4 95 9777 9782 9786 9791 9795 9800 9805 9809 9814 9818 0 1 1 2 2 3 3 4 4 96 9823 9827 9832 9836 9841 9845 9850 9854 9859 9863 0 1 1 2 2 3 3 4 4 97 9868 9872 9877 9881 9886 9890 9894 9899 9903 9908 0 1 1 2 2 3 3 4 4 98 9912 9917 9921 9926 9930 9934 9939 9943 9948 9952 0 1 1 2 2 3 3 4 4 99 9956 9961 9965 9969 9974 9978 9983 9987 9991 9996 0 1 1 2 2 3 3 3 4   [ H O M E ] [ S C I E N C E ] [ M A T H S ] [ A S T R O N O M Y ] Download | Shop | Contact | About   Page compiled: Wed Sep 05 18:37:57 GMT+01:00 2001