# How do you solve log_(1/10)x=-3 and check the solutions?

Jun 22, 2018

$x = 1000$

#### Explanation:

We use that

${\log}_{a} \left(b\right) = n$ if ${a}^{n} = b$
then we get

${\left(\frac{1}{10}\right)}^{- 3} = x$
$x = 1000$
Checking the solution:

$\ln \frac{1000}{\ln} \left(\frac{1}{10}\right) = \frac{3 \ln \left(10\right)}{\ln} \left({10}^{- 1}\right) = - 3$