Algebra
Intermediate

Logarithm Quotient Rule

The logarithm of a quotient equals the difference of logarithms.

Formula

log⁡b(xy)=log⁡b(x)−log⁡b(y)\log_b\left(\frac{x}{y}\right) = \log_b(x) - \log_b(y)

Variables

bBase
x, yPositive reals

Example

log₂(8/2) = log₂ 8 − log₂ 2 = 3 − 1 = 2.

Did You Know?

Before calculators, slide rules used this rule physically — sliding two logarithmic scales to divide numbers.

logarithmquotientlog rules