Precalculus Examples

$\log_{2} (\sqrt[4]{8})$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{8}$ as $8^{\frac{1}{4}}$ .

$\log_{2} (8^{\frac{1}{4}})$

Step 2

Expand $\log_{2} (8^{\frac{1}{4}})$ by moving $\frac{1}{4}$ outside the logarithm.

$\frac{1}{4} \log_{2} (8)$

Step 3

Logarithm base $2$ of $8$ is $3$ .

$\frac{1}{4} \cdot 3$

Step 4

Combine $\frac{1}{4}$ and $3$ .

$\frac{3}{4}$