Precalculus Examples

$2 \log_{9} (\sqrt[5]{81})$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[5]{81}$ as $81^{\frac{1}{5}}$ .

$2 \log_{9} (81^{\frac{1}{5}})$

Step 2

Expand $\log_{9} (81^{\frac{1}{5}})$ by moving $\frac{1}{5}$ outside the logarithm.

$2 (\frac{1}{5} \log_{9} (81))$

Step 3

Logarithm base $9$ of $81$ is $2$ .

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

Step 4

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

$2 (\frac{2}{5})$

Step 5

Multiply $2 (\frac{2}{5})$ .

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Step 5.1

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

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

Step 5.2

Multiply $2$ by $2$ .

$\frac{4}{5}$