Precalculus Examples

$\log_{3} (\sqrt[5]{3})$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[5]{3}$ as $3^{\frac{1}{5}}$ .

$\log_{3} (3^{\frac{1}{5}})$

Step 2

Expand $\log_{3} (3^{\frac{1}{5}})$ by moving $\frac{1}{5}$ outside the logarithm.

$\frac{1}{5} \log_{3} (3)$

Step 3

Logarithm base $3$ of $3$ is $1$ .

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

Step 4

Multiply $\frac{1}{5}$ by $1$ .

$\frac{1}{5}$