Logarithm Calculator
Calculate logarithms in any base, convert between bases, and explore properties.
Calculate logarithm
log10(100)
log10(100)
2.000000
log₁₀
2.0000
ln
4.6052
log₂
6.6439
Verification
102.000000 = 100.000000
The result should be approximately equal to the original value
Common values
| x | log₁₀ | ln | log₂ |
|---|---|---|---|
| 1 | 0.0000 | 0.0000 | 0.0000 |
| 2 | 0.3010 | 0.6931 | 1.0000 |
| 5 | 0.6990 | 1.6094 | 2.3219 |
| 10 | 1.0000 | 2.3026 | 3.3219 |
| 20 | 1.3010 | 2.9957 | 4.3219 |
| 50 | 1.6990 | 3.9120 | 5.6439 |
| 100 | 2.0000 | 4.6052 | 6.6439 |
| 1000 | 3.0000 | 6.9078 | 9.9658 |
| 10000 | 4.0000 | 9.2103 | 13.2877 |
What is a logarithm?
Logarithm is the inverse operation of exponentiation. logₐ(x) answers: to what power must 'a' be raised to get 'x'? For example, log₂(8) = 3 because 2³ = 8.
Types of logarithms
log₁₀ (common): base 10, used in sciences. ln (natural): base e ≈ 2.718, fundamental in calculus. log₂ (binary): used in computing and information theory.
Applications
Logarithmic scales (pH, decibels, Richter), algorithmic complexity, compound interest, growth/decay, data compression, and signal processing.