# How do you solve log_5 2x − 5 = −4?

May 4, 2016

$x = \frac{1563}{625}$

#### Explanation:

Use definition ${\log}_{b} x = y \iff {b}^{y} = x$

${5}^{-} 4 = 2 x - 5$

$\frac{1}{5} ^ 4 = 2 x - 5$

$\frac{1}{625} = 2 x - 5$

$\frac{1}{625} + 5 = 2 x$

$\frac{3126}{625} = 2 x$

$x = \frac{1563}{625}$