Calculus Examples

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

Step 1

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

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

Step 2

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

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

Step 3

Logarithm base $5$ of $25$ is $2$ .

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

Step 4

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

$\frac{2}{3}$