# How do you solve 20^(n-2)+6.5=87?

Jun 15, 2018

$n = \frac{\ln \left(80.5\right) + 2 \ln \left(20\right)}{\ln} \left(20\right)$

#### Explanation:

First, we subtract 6.5 from both sides to get
${20}^{n - 2} = 80.5$
Taking the natural log (or whatever base you choose), we get
$\left(n - 2\right) \ln \left(20\right) = \ln \left(80.5\right)$
$n \ln \left(20\right) - 2 \ln \left(20\right) = \ln \left(80.5\right)$
$n \ln \left(20\right) = \ln \left(80.5\right) + 2 \ln \left(20\right)$
$n = \frac{\ln \left(80.5\right) + 2 \ln \left(20\right)}{\ln} \left(20\right)$