Algebra
Advanced

Change of Base

Convert a logarithm to a different base.

Formula

log⁡bx=log⁡kxlog⁡kb\log_b x = \frac{\log_k x}{\log_k b}

Variables

bOriginal base
kNew base
xArgument

Example

log_2(8)=ln8/ln2=3

Did You Know?

The change-of-base formula lets a calculator with only log and ln buttons compute a logarithm in any base at all.

logarithm