Precalculus Examples

$\log_{6} (\sqrt[3]{6})$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{6}$ as $6^{\frac{1}{3}}$ .

$\log_{6} (6^{\frac{1}{3}})$

Step 2

Expand $\log_{6} (6^{\frac{1}{3}})$ by moving $\frac{1}{3}$ outside the logarithm.

$\frac{1}{3} \log_{6} (6)$

Step 3

Logarithm base $6$ of $6$ is $1$ .

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

Step 4

Multiply $\frac{1}{3}$ by $1$ .

$\frac{1}{3}$