Precalculus Examples

$\log_{8} (\frac{1}{\sqrt[5]{64}})$

Step 1

Rewrite $\log_{8} (\frac{1}{\sqrt[5]{64}})$ as $\log_{8} (1) - \log_{8} (\sqrt[5]{64})$ .

$\log_{8} (1) - \log_{8} (\sqrt[5]{64})$

Step 2

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[5]{64}$ as $64^{\frac{1}{5}}$ .

$\log_{8} (1) - \log_{8} (64^{\frac{1}{5}})$

Step 3

Expand $\log_{8} (64^{\frac{1}{5}})$ by moving $\frac{1}{5}$ outside the logarithm.

$\log_{8} (1) - (\frac{1}{5} \log_{8} (64))$

Step 4

Logarithm base $8$ of $1$ is $0$ .

$0 - (\frac{1}{5} \log_{8} (64))$

Step 5

Logarithm base $8$ of $64$ is $2$ .

$0 - (\frac{1}{5} \cdot 2)$

Step 6

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

$0 - \frac{2}{5}$

Step 7

Subtract $\frac{2}{5}$ from $0$ .

$- \frac{2}{5}$