# How do you solve 9^(8x)=13^(-x+7)?

Feb 27, 2016

$x = 7 - 8 \log \frac{9}{\log} \left(13\right)$

#### Explanation:

${9}^{8 x} = {13}^{- x + 7}$

You need to use logarithms:

$8 x . \log \left(9\right) = \left(- x + 7\right) \log \left(13\right)$

$8 \log \frac{9}{\log} \left(13\right) = - x + 7$

$x = 7 - 8 \log \frac{9}{\log} \left(13\right)$

It is a very ugly solution.