Algebra
Intermediate

Change of Base Formula

Converts a logarithm from one base to another.

Formula

log⁡b(x)=log⁡k(x)log⁡k(b)\log_b(x) = \frac{\log_k(x)}{\log_k(b)}

Variables

bOriginal base
kNew base
xArgument

Example

log₂ 10 = log₁₀ 10 / log₁₀ 2 = 1 / 0.301 ≈ 3.32.

Did You Know?

This trick lets a calculator with only log and ln buttons compute a logarithm in any base at all.

logarithmchange of base