How do you solve 5^(-9.2x-9)-4=57?

Nov 18, 2016

Isolate the term involving the variable, then take the ${\log}_{5}$ of both sides.

Explanation:

${5}^{- 9.2 x - 9} - 4 = 57$

${5}^{- 9.2 x - 9} = 61$

${\log}_{5} \left({5}^{- 9.2 x - 9}\right) = {\log}_{5} 61$

$- 9.2 x - 9 = {\log}_{5} 61$

$- 9.2 x = {\log}_{5} 61 + 9$

$x = - \frac{{\log}_{5} 61 + 9}{9.2}$

$\left(x \approx - 1.2559\right)$