How to work it out
- Write 16 = 2⁴.
- Use log(ab) = log a + log b and log(aᵏ) = k log a: log 16 = 4 log 2.
- = 4 × 0.3010 = 1.2041.
- For the natural log, multiply by 2.303: ln 16 = 2.303 × 1.2041 ≈ 2.7726.
Log values from 1 to 20
| Number | log₁₀ (log) | logₑ (ln) |
|---|---|---|
| log 1 | 0.0000 | 0.0000 |
| log 2 | 0.3010 | 0.6931 |
| log 3 | 0.4771 | 1.0986 |
| log 4 | 0.6021 | 1.3863 |
| log 5 | 0.6990 | 1.6094 |
| log 6 | 0.7782 | 1.7918 |
| log 7 | 0.8451 | 1.9459 |
| log 8 | 0.9031 | 2.0794 |
| log 9 | 0.9542 | 2.1972 |
| log 10 | 1.0000 | 2.3026 |
| log 11 | 1.0414 | 2.3979 |
| log 12 | 1.0792 | 2.4849 |
| log 13 | 1.1139 | 2.5649 |
| log 14 | 1.1461 | 2.6391 |
| log 15 | 1.1761 | 2.7081 |
| log 16 | 1.2041 | 2.7726 |
| log 17 | 1.2304 | 2.8332 |
| log 18 | 1.2553 | 2.8904 |
| log 19 | 1.2788 | 2.9444 |
| log 20 | 1.3010 | 2.9957 |
| log 25 | 1.3979 | 3.2189 |
| log 30 | 1.4771 | 3.4012 |
| log 50 | 1.6990 | 3.9120 |
| log 100 | 2.0000 | 4.6052 |
| log e | 0.4343 | 1.0000 |
For any other number, use the four-figure log table or the antilog table to go back.
Questions students ask
What is the value of log 16?
log 16 (base 10) = 1.2041. The natural log, ln 16, is 2.7726.
What is the value of ln 16?
ln 16 = logₑ16 = 2.7726.
How do you find log 16 without a calculator?
Write 16 = 2⁴. Use log(ab) = log a + log b and log(aᵏ) = k log a: log 16 = 4 log 2. = 4 × 0.3010 = 1.2041. For the natural log, multiply by 2.303: ln 16 = 2.303 × 1.2041 ≈ 2.7726.