Log Calculator
Calculate logarithms in any base — log₁₀ (common log), ln (natural log), log₂ (binary log), or any custom base. Also calculate antilogarithms.
Logarithm
| Function | Notation | Result |
|---|
| Common log | log₁₀(100) | 2 |
| Natural log | ln(100) | 4.605170186 |
| Binary log | log₂(100) | 6.6438561898 |
| Custom base | log5(100) | 2.8613531161 |
Log Reference Table
| Number | log₁₀ | ln | log₂ |
|---|
| 0.001 | -3 | -6.907755279 | -9.9657842847 |
| 0.01 | -2 | -4.605170186 | -6.6438561898 |
| 0.1 | -1 | -2.302585093 | -3.3219280949 |
| 1 | 0 | 0 | 0 |
| 2 | 0.3010299957 | 0.6931471806 | 1 |
| e | 0.4342944819 | 1 | 1.4426950409 |
| 10 | 1 | 2.302585093 | 3.3219280949 |
| 100 | 2 | 4.605170186 | 6.6438561898 |
| 1000 | 3 | 6.907755279 | 9.9657842847 |
| Property | Rule |
|---|
| Product rule | log(ab) = log(a) + log(b) |
| Quotient rule | log(a/b) = log(a) − log(b) |
| Power rule | log(aⁿ) = n · log(a) |
| Change of base | logb(x) = ln(x) / ln(b) |
| logb(1) | = 0 for any base b |
| logb(b) | = 1 for any base b |