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

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

Step 1

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

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

Step 2

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

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

Step 3

Combine $\frac{1}{3}$ and $\log_{2} (x)$ .

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