# How do you solve x= \log _ { 10} \root(6) { 10}?

Mar 4, 2018

$x = \frac{1}{6}$

#### Explanation:

We know that

${\log}_{10} \left({10}^{a}\right) = a$

So it would be nice to get our equation in a form like that. We need to recall that a root is the same as the reciprocal of the power, i.e.:

$\setminus \sqrt[b]{y} = {y}^{\frac{1}{b}}$

Therefore:

$x = {\log}_{10} \left(\setminus \sqrt[6]{10}\right) = {\log}_{10} \left({10}^{\frac{1}{6}}\right) = \frac{1}{6}$