# How do you solve 4^( x + 2) = 20?

May 28, 2016

I found: $x = \frac{\ln \left(20\right)}{\ln \left(4\right)} - 2 = 0.16096$

#### Explanation:

I would first take the natural log of both sides:
$\ln {\left(4\right)}^{x + 2} = \ln \left(20\right)$
then use a property of logs to write:
$\left(x + 2\right) \ln \left(4\right) = \ln \left(20\right)$
rearrange:
$x + 2 = \frac{\ln \left(20\right)}{\ln \left(4\right)}$
and:
$x = \frac{\ln \left(20\right)}{\ln \left(4\right)} - 2 = 0.16096$