Expand the Logarithmic Expression log base 2 of cube root of 2

$\log_{2} (\sqrt[3]{2})$

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{2}$ as $2^{\frac{1}{3}}$ .

$\log_{2} (2^{\frac{1}{3}})$

Expand $\log_{2} (2^{\frac{1}{3}})$ by moving $\frac{1}{3}$ outside the logarithm.

$\frac{1}{3} \log_{2} (2)$

Logarithm base $2$ of $2$ is $1$ .

$\frac{1}{3} \cdot 1$

Multiply $\frac{1}{3}$ by $1$ .

$\frac{1}{3}$