Evaluate log base 6 of cube root of 6

$\log_{6} (\sqrt[3]{6})$

The change of base rule can be used if $a$ and $b$ are greater than $0$ and not equal to $1$ , and $x$ is greater than $0$ .

$\log_{a} (x) = \frac{\log_{b} (x)}{\log_{b} (a)}$

Substitute in values for the variables in the change of base formula, using $b = 10$ .

$\frac{\log (\sqrt[3]{6})}{\log (6)}$

The result can be shown in multiple forms.

Exact Form:

$\frac{\log (\sqrt[3]{6})}{\log (6)}$

Decimal Form:

$0.\overline{3}$