Precalculus Examples

$\log_{4} (\frac{1}{\sqrt[3]{16}})$

Step 1

Rewrite $\log_{4} (\frac{1}{\sqrt[3]{16}})$ as $\log_{4} (1) - \log_{4} (\sqrt[3]{16})$ .

$\log_{4} (1) - \log_{4} (\sqrt[3]{16})$

Step 2

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{16}$ as $16^{\frac{1}{3}}$ .

$\log_{4} (1) - \log_{4} (16^{\frac{1}{3}})$

Step 3

Expand $\log_{4} (16^{\frac{1}{3}})$ by moving $\frac{1}{3}$ outside the logarithm.

$\log_{4} (1) - (\frac{1}{3} \log_{4} (16))$

Step 4

Logarithm base $4$ of $1$ is $0$ .

$0 - (\frac{1}{3} \log_{4} (16))$

Step 5

Logarithm base $4$ of $16$ is $2$ .

$0 - (\frac{1}{3} \cdot 2)$

Step 6

Combine $\frac{1}{3}$ and $2$ .

$0 - \frac{2}{3}$

Step 7

Subtract $\frac{2}{3}$ from $0$ .

$- \frac{2}{3}$