Algebra
Intermediate

Logarithm Power Rule

The log of a power brings the exponent to the front.

Formula

log⁡b(xn)=nlog⁡bx\log_b(x^n) = n\log_b x

Variables

bBase
xArgument
nExponent

Example

log(1000)=3log(10)=3

Did You Know?

This rule is why logarithmic scales compress enormous ranges — earthquakes and sound levels both rely on it.

logarithm