# How do you evaluate log_81 9?

Aug 16, 2016

Use the change of base formula to find:

${\log}_{81} 9 = \frac{1}{2}$

#### Explanation:

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

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

So we find:

${\log}_{81} 9 = {\log}_{9} \frac{9}{\log} _ 9 81 = {\log}_{9} \frac{9}{\log} _ 9 {9}^{2} = \frac{1}{2}$