Base Power Law of Logarithms

Formula

$\log_{b^n}{m}$ $\,=\,$ $\Big(\dfrac{1}{n}\Big)\log_{b}{m}$

The logarithm of a quantity can be calculated by expressing the base quantity in exponential form and then divide the logarithm of quantity to base of exponential term by the exponent.

The identity of base power rule of logarithm is often used to calculate logarithm of quantities when there is a possibility to express base quantities in exponential notation.

Proof

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