# Power Law of Logarithms

## Formula

$\log_{b}{(m^{\displaystyle n})}$ $\,=\,$ $n\log_{b}{m}$

Logarithm of a quantity can be evaluated by expressing the quantity in exponential form by using power rule of logarithms. It is actually done by multiplying the exponent with logarithm of base of quantity in exponential form.

The identity of Power rule of logarithms is mostly used in dealing quantities which can be expressed in exponential notation.

### Proof

Learn how to derive the property of power rule of logarithms in algebraic form.

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