Algebra
Intermediate

Logarithm Product Rule

The logarithm of a product equals the sum of logarithms.

Formula

log⁡b(xy)=log⁡b(x)+log⁡b(y)\log_b(xy) = \log_b(x) + \log_b(y)

Variables

bBase
x, yPositive reals

Example

log₂(8×4) = 3 + 2 = 5

Did You Know?

Logarithms turned multiplication into addition, and were called "a device that doubled the lifespan of astronomers" by cutting their calculation time.

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