Precalculus Examples

$\log_{7} (\sqrt[5]{49})$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[5]{49}$ as $49^{\frac{1}{5}}$ .

$\log_{7} (49^{\frac{1}{5}})$

Step 2

Expand $\log_{7} (49^{\frac{1}{5}})$ by moving $\frac{1}{5}$ outside the logarithm.

$\frac{1}{5} \log_{7} (49)$

Step 3

Logarithm base $7$ of $49$ is $2$ .

$\frac{1}{5} \cdot 2$

Step 4

Combine $\frac{1}{5}$ and $2$ .

$\frac{2}{5}$