# How do you solve log_4 (x-6)^3= 6?

Nov 7, 2015

$x = 22$

#### Explanation:

By using laws of logs we can write this equation as :

$3 {\log}_{4} \left(x - 6\right) = 6$

Now divide throughout by 3 to get

${\log}_{4} \left(x - 6\right) = 2$

Now applying the definition of log, we get

$x - 6 = {4}^{2}$

$\therefore x = 22$