# What is x if log(5x) = -3?

Oct 24, 2015

$\frac{1}{5000}$

#### Explanation:

From the definition of logs,
$y = {\log}_{a} x \iff {a}^{y} = x$

we may write this equation as

${\log}_{10} \left(5 x\right) = - 3 \iff {10}^{- 3} = 5 x$

$\therefore x = {10}^{- 3} / 5 = \frac{1}{5000}$