Precalculus Examples

$\log_{7} (\sqrt[3]{7})$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{7}$ as $7^{\frac{1}{3}}$ .

$\log_{7} (7^{\frac{1}{3}})$

Step 2

Expand $\log_{7} (7^{\frac{1}{3}})$ by moving $\frac{1}{3}$ outside the logarithm.

$\frac{1}{3} \log_{7} (7)$

Step 3

Logarithm base $7$ of $7$ is $1$ .

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

Step 4

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

$\frac{1}{3}$