Apr 15, 2017

$\log {6}^{\frac{1}{3}}$

#### Explanation:

Using the $\textcolor{b l u e}{\text{law of logarithms}}$

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{\log {x}^{n} \Leftrightarrow n \log x} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\Rightarrow \frac{\log 6}{3} = \frac{1}{3} \log 6 = \log {6}^{\frac{1}{3}}$

Apr 15, 2017

#### Explanation:

Given: $\frac{\log \left(6\right)}{3}$

The above can be written as:

$\left(\frac{1}{3}\right) \log \left(6\right)$

Use the property of logarithms $\left(c\right) \log \left(a\right) = \log \left({a}^{c}\right)$:

$\log \left({6}^{\frac{1}{3}}\right)$

We know that the $\frac{1}{3}$ power is the same as the cube root:

$\log \left(\sqrt[3]{6}\right) \leftarrow$ the answer.