# What is log_81 3 ?

Aug 28, 2016

${\log}_{81} 3 = \frac{1}{4}$

#### Explanation:

The change of base formula tells us that for $a , b , c > 0$ with $a \ne 1$ and $c \ne 1$ we have:

${\log}_{a} b = {\log}_{c} \frac{b}{\log} _ c a$

Hence we find:

${\log}_{81} 3 = {\log}_{3} \frac{3}{\log} _ 3 81 = {\log}_{3} \frac{3}{\log} _ 3 {3}^{4} = \frac{1}{4}$