# How do you solve log_x 6 = 0.5?

Jan 8, 2016

You solve any simple log equation by putting the equation back into exponential form.

#### Explanation:

Essentially this question is asking you base $x$ to exponent $\frac{1}{2}$ is 6.

${\log}_{x} 6 = 0.5$
To put this into exponential form, write it like ${x}^{0.5} = 6$.
Which is $\sqrt{x} = 6$
The inverse operation of square root is ${x}^{2}$, so simply square both sides to get your answer.

${\left(\sqrt{x}\right)}^{2} = {6}^{2}$
$x = 36$