# How do you solve -5*2^(-7n-7)+5=-66?

Mar 4, 2017

$n = - 1 - \sqrt[7]{{\log}_{2} \left(\frac{71}{5}\right)}$

#### Explanation:

You would subtract 5 and divide all by -5:

$- 5 \cdot {2}^{- 7 n - 7} = - 71$

${2}^{- 7 n - 7} = \frac{71}{5}$

then it is

$- 7 n - 7 = {\log}_{2} \left(\frac{71}{5}\right)$

$- 7 n = 7 + {\log}_{2} \left(\frac{71}{5}\right)$

$n = - 1 - \frac{1}{7} {\log}_{2} \left(\frac{71}{5}\right)$

$n = - 1 - \sqrt[7]{{\log}_{2} \left(\frac{71}{5}\right)}$