# Double Power Law of Logarithms

## Formula

$\log_{b^y}{m^x}$ $\,=\,$ $\Big(\dfrac{x}{y}\Big)\log_{b}{m}$

Logarithm of a quantity can be calculated by expressing quantity and base quantity of logarithmic term in exponential form, then the value of product of quotient of exponent of quantity by exponent of base quantity and log of base of quantity to base of base quantity gives the logarithm of quantity.

This mathematical identity is called as double power rule property of logarithms and it is used as a formula when the quantity and base quantity of logarithmic term are expressed in exponential notation.

### Proof

Learn how to derive property of double power rule of logarithms in algebraic form when quantity and base quantity of log term are written in exponential form.

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