# How do you solve log_10 x=-1?

Feb 27, 2016

Take $10$ to the power of each side of the equation to find that

$x = \frac{1}{10}$

#### Explanation:

By their definition, logarithms have the property that ${a}^{{\log}_{a} \left(x\right)} = x$

Using that, we have

${\log}_{10} \left(x\right) = - 1$

$\implies {10}^{{\log}_{10} \left(x\right)} = {10}^{- 1}$

$\implies x = {10}^{- 1} = \frac{1}{10}$