# How do you solve 4^x = 12?

##### 1 Answer
Mar 11, 2018

$x = 1.79$

#### Explanation:

Apply the ${\log}_{4}$ on both sides of the equation

${\log}_{4} \left({4}^{x}\right) = {\log}_{4} \left(12\right)$

Apply an Exponent Logarithm Law:
$x \cdot {\log}_{4} \left(4\right) = {\log}_{4} \left(12\right)$

${\log}_{a} \left(a\right)$ always equals 1, so you get:
$x = {\log}_{4} \left(12\right)$

If your calculator doesn't have log bases besides the default (10) you can apply the change of base formula:
$x = \log \frac{12}{\log} \left(4\right)$