# How do you solve 5^(x+2) = 8.5?

Mar 12, 2016

$x = {\log}_{5} \left(0.34\right)$

#### Explanation:

${5}^{x + 2} = 8.5$

If we apply logarithms, we obtain:

$x + 2 = {\log}_{5} \left(8.5\right)$

$x = {\log}_{5} \left(8.5\right) - 2$

$x = {\log}_{5} \left(8.5\right) - {\log}_{5} \left({5}^{-} 2\right)$

$x = {\log}_{5} \left(\frac{8.5}{25}\right)$

$x = {\log}_{5} \left(0.34\right)$

or $x = \ln \frac{0.34}{\ln} \left(5\right)$