log₁₀ 2 = 0.3010, ln 2 = 0.6931 and ln 10 = 2.3026. The log of any number from 1 to 100 lies between 0 and 2.
- log₁₀ n
- ln n
| n | log₁₀ n | ln n | log₂ n |
|---|---|---|---|
| 1 | 0.0000 | 0.0000 | 0.0000 |
| 2 | 0.3010 | 0.6931 | 1.0000 |
| 3 | 0.4771 | 1.0986 | 1.5850 |
| 4 | 0.6021 | 1.3863 | 2.0000 |
| 5 | 0.6990 | 1.6094 | 2.3219 |
| 6 | 0.7782 | 1.7918 | 2.5850 |
| 7 | 0.8451 | 1.9459 | 2.8074 |
| 8 | 0.9031 | 2.0794 | 3.0000 |
| 9 | 0.9542 | 2.1972 | 3.1699 |
| 10 | 1.0000 | 2.3026 | 3.3219 |
| 11 | 1.0414 | 2.3979 | 3.4594 |
| 12 | 1.0792 | 2.4849 | 3.5850 |
| 13 | 1.1139 | 2.5649 | 3.7004 |
| 14 | 1.1461 | 2.6391 | 3.8074 |
| 15 | 1.1761 | 2.7081 | 3.9069 |
| 16 | 1.2041 | 2.7726 | 4.0000 |
| 17 | 1.2304 | 2.8332 | 4.0875 |
| 18 | 1.2553 | 2.8904 | 4.1699 |
| 19 | 1.2788 | 2.9444 | 4.2479 |
| 20 | 1.3010 | 2.9957 | 4.3219 |
| 21 | 1.3222 | 3.0445 | 4.3923 |
| 22 | 1.3424 | 3.0910 | 4.4594 |
| 23 | 1.3617 | 3.1355 | 4.5236 |
| 24 | 1.3802 | 3.1781 | 4.5850 |
| 25 | 1.3979 | 3.2189 | 4.6439 |
| 26 | 1.4150 | 3.2581 | 4.7004 |
| 27 | 1.4314 | 3.2958 | 4.7549 |
| 28 | 1.4472 | 3.3322 | 4.8074 |
| 29 | 1.4624 | 3.3673 | 4.8580 |
| 30 | 1.4771 | 3.4012 | 4.9069 |
| 31 | 1.4914 | 3.4340 | 4.9542 |
| 32 | 1.5051 | 3.4657 | 5.0000 |
| 33 | 1.5185 | 3.4965 | 5.0444 |
| 34 | 1.5315 | 3.5264 | 5.0875 |
| 35 | 1.5441 | 3.5553 | 5.1293 |
| 36 | 1.5563 | 3.5835 | 5.1699 |
| 37 | 1.5682 | 3.6109 | 5.2095 |
| 38 | 1.5798 | 3.6376 | 5.2479 |
| 39 | 1.5911 | 3.6636 | 5.2854 |
| 40 | 1.6021 | 3.6889 | 5.3219 |
| 41 | 1.6128 | 3.7136 | 5.3576 |
| 42 | 1.6232 | 3.7377 | 5.3923 |
| 43 | 1.6335 | 3.7612 | 5.4263 |
| 44 | 1.6435 | 3.7842 | 5.4594 |
| 45 | 1.6532 | 3.8067 | 5.4919 |
| 46 | 1.6628 | 3.8286 | 5.5236 |
| 47 | 1.6721 | 3.8501 | 5.5546 |
| 48 | 1.6812 | 3.8712 | 5.5850 |
| 49 | 1.6902 | 3.8918 | 5.6147 |
| 50 | 1.6990 | 3.9120 | 5.6439 |
| 51 | 1.7076 | 3.9318 | 5.6724 |
| 52 | 1.7160 | 3.9512 | 5.7004 |
| 53 | 1.7243 | 3.9703 | 5.7279 |
| 54 | 1.7324 | 3.9890 | 5.7549 |
| 55 | 1.7404 | 4.0073 | 5.7814 |
| 56 | 1.7482 | 4.0254 | 5.8074 |
| 57 | 1.7559 | 4.0431 | 5.8329 |
| 58 | 1.7634 | 4.0604 | 5.8580 |
| 59 | 1.7709 | 4.0775 | 5.8826 |
| 60 | 1.7782 | 4.0943 | 5.9069 |
| 61 | 1.7853 | 4.1109 | 5.9307 |
| 62 | 1.7924 | 4.1271 | 5.9542 |
| 63 | 1.7993 | 4.1431 | 5.9773 |
| 64 | 1.8062 | 4.1589 | 6.0000 |
| 65 | 1.8129 | 4.1744 | 6.0224 |
| 66 | 1.8195 | 4.1897 | 6.0444 |
| 67 | 1.8261 | 4.2047 | 6.0661 |
| 68 | 1.8325 | 4.2195 | 6.0875 |
| 69 | 1.8388 | 4.2341 | 6.1085 |
| 70 | 1.8451 | 4.2485 | 6.1293 |
| 71 | 1.8513 | 4.2627 | 6.1497 |
| 72 | 1.8573 | 4.2767 | 6.1699 |
| 73 | 1.8633 | 4.2905 | 6.1898 |
| 74 | 1.8692 | 4.3041 | 6.2095 |
| 75 | 1.8751 | 4.3175 | 6.2288 |
| 76 | 1.8808 | 4.3307 | 6.2479 |
| 77 | 1.8865 | 4.3438 | 6.2668 |
| 78 | 1.8921 | 4.3567 | 6.2854 |
| 79 | 1.8976 | 4.3694 | 6.3038 |
| 80 | 1.9031 | 4.3820 | 6.3219 |
| 81 | 1.9085 | 4.3944 | 6.3399 |
| 82 | 1.9138 | 4.4067 | 6.3576 |
| 83 | 1.9191 | 4.4188 | 6.3750 |
| 84 | 1.9243 | 4.4308 | 6.3923 |
| 85 | 1.9294 | 4.4427 | 6.4094 |
| 86 | 1.9345 | 4.4543 | 6.4263 |
| 87 | 1.9395 | 4.4659 | 6.4429 |
| 88 | 1.9445 | 4.4773 | 6.4594 |
| 89 | 1.9494 | 4.4886 | 6.4757 |
| 90 | 1.9542 | 4.4998 | 6.4919 |
| 91 | 1.9590 | 4.5109 | 6.5078 |
| 92 | 1.9638 | 4.5218 | 6.5236 |
| 93 | 1.9685 | 4.5326 | 6.5392 |
| 94 | 1.9731 | 4.5433 | 6.5546 |
| 95 | 1.9777 | 4.5539 | 6.5699 |
| 96 | 1.9823 | 4.5643 | 6.5850 |
| 97 | 1.9868 | 4.5747 | 6.5999 |
| 98 | 1.9912 | 4.5850 | 6.6147 |
| 99 | 1.9956 | 4.5951 | 6.6294 |
| 100 | 2.0000 | 4.6052 | 6.6439 |
How it is computed
log₁₀ n is the power of 10 that gives n, ln n the power of e (≈ 2.71828) and log₂ n the power of 2. The three differ only by a constant factor: ln n = log₁₀ n × ln 10. Values are rounded to four decimals.
FAQ
How do I get the log of a number above 100?+
Factor out powers of ten: log₁₀ 2,500 = log₁₀ 25 + 2. This is how printed log tables were used before calculators.
What is the log of 0 or a negative number?+
It is undefined: no power of a positive base gives 0 or a negative result. As n approaches 0, the log falls toward minus infinity.