# How do you solve x=log_36 6?

Nov 30, 2015

Use the change of base formula and basic properties of logs to find:

$x = \frac{1}{2}$

#### Explanation:

If $a , b , c > 0$ then ${\log}_{a} b = \frac{{\log}_{c} b}{{\log}_{c} a}$

So:

${\log}_{36} 6 = \frac{\log 6}{\log 36} = \frac{\log 6}{\log {6}^{2}} = \frac{\log 6}{2 \log 6} = \frac{1}{2}$