How do you solve 8^(-5a)-5=53?

Oct 7, 2016

$a = - 0.391$

Explanation:

${8}^{- 5 a} - 5 = 53$

$\Leftrightarrow {8}^{- 5 a} = 53 + 5 = 58$

ot ${\log}_{8} \left(58\right) = - 5 a$

or $a = - \frac{1}{5} \times {\log}_{8} \left(58\right) = - \frac{1}{5} \times \log \frac{58}{\log} 8$

i.e. $a = - \frac{1}{5} \times \frac{1.763428}{0.90309} = - 0.391$