Log Calculator
Enter a positive number to get log base 10, natural log (ln), log base 2, and any custom base.
Logarithm — Guide
What is a logarithm?
logᵉ(x) = y ⇔ by = x — "To what power must b be raised to get x?"
Key identities
log(a × b) = log a + log b • log(a / b) = log a − log b • log(an) = n × log a
Change of base
logᵉ(x) = ln(x) / ln(b) = log₁₀(x) / log₁₀(b)
Quick reference
| x | log₁₀(x) | ln(x) | log₂(x) |
|---|---|---|---|
| 1 | 0 | 0 | 0 |
| 2 | 0.301 | 0.693 | 1 |
| 10 | 1 | 2.303 | 3.322 |
| 100 | 2 | 4.605 | 6.644 |
| 1000 | 3 | 6.908 | 9.966 |
