Precalculus Examples

$\log_{5} (\sqrt[4]{17})$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{17}$ as $17^{\frac{1}{4}}$ .

$\log_{5} (17^{\frac{1}{4}})$

Step 2

Expand $\log_{5} (17^{\frac{1}{4}})$ by moving $\frac{1}{4}$ outside the logarithm.

$\frac{1}{4} \log_{5} (17)$

Step 3

Combine $\frac{1}{4}$ and $\log_{5} (17)$ .

$\frac{\log_{5} (17)}{4}$