# 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.

Latest Math Topics

A best free mathematics education website for students, teachers and researchers.

###### Maths Topics

Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.

###### Maths Problems

Learn how to solve the maths problems in different methods with understandable steps.

Learn solutions

###### Subscribe us

You can get the latest updates from us by following to our official page of Math Doubts in one of your favourite social media sites.