Precalculus Examples

$\log_{5} (\sqrt[3]{\frac{1}{25}})$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{\frac{1}{25}}$ as ${(\frac{1}{25})}^{\frac{1}{3}}$ .

$\log_{5} ({(\frac{1}{25})}^{\frac{1}{3}})$

Step 2

Expand $\log_{5} ({(\frac{1}{25})}^{\frac{1}{3}})$ by moving $\frac{1}{3}$ outside the logarithm.

$\frac{1}{3} \log_{5} (\frac{1}{25})$

Step 3

Logarithm base $5$ of $\frac{1}{25}$ is $- 2$ .

$\frac{1}{3} \cdot - 2$

Step 4

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

$\frac{- 2}{3}$

Step 5

Move the negative in front of the fraction.

$- \frac{2}{3}$