# How do you solve log_x(1/256)=-4?

Jul 28, 2018

The answer is $x = 4$

#### Explanation:

The equation is

${\log}_{x} \left(\frac{1}{256}\right) = - 4$

By the definition of logs

${x}^{- 4} = \frac{1}{256} = \frac{1}{2} ^ 8 = {2}^{- 8}$

So,

$\frac{1}{x} ^ - 4 = \frac{1}{2} ^ - 8$

${x}^{4} = {2}^{8}$

$x = {2}^{\frac{8}{4}} = {2}^{2} = 4$