Algebra
Intermediate

Logarithm Power Rule

The logarithm of a power equals the exponent times the logarithm.

Formula

log⁡b(xn)=n⋅log⁡b(x)\log_b(x^n) = n \cdot \log_b(x)

Variables

bBase
xPositive real
nExponent

Example

log₂(8³) = 3·log₂ 8 = 3×3 = 9.

Did You Know?

This rule is why log scales handle enormous ranges — raising to a power just multiplies the log.

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