Precalculus Examples

$\log_{4} (\sqrt[5]{16})$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[5]{16}$ as $16^{\frac{1}{5}}$ .

$\log_{4} (16^{\frac{1}{5}})$

Step 2

Expand $\log_{4} (16^{\frac{1}{5}})$ by moving $\frac{1}{5}$ outside the logarithm.

$\frac{1}{5} \log_{4} (16)$

Step 3

Logarithm base $4$ of $16$ is $2$ .

$\frac{1}{5} \cdot 2$

Step 4

Combine $\frac{1}{5}$ and $2$ .

$\frac{2}{5}$