Precalculus Examples

$\ln (\sqrt[8]{e^{3}})$

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[8]{e^{3}}$ as $e^{\frac{3}{8}}$ .

$\ln (e^{\frac{3}{8}})$

Expand $\ln (e^{\frac{3}{8}})$ by moving $\frac{3}{8}$ outside the logarithm.

$\frac{3}{8} \ln (e)$

The natural logarithm of $e$ is $1$ .

$\frac{3}{8} \cdot 1$

Multiply $\frac{3}{8}$ by $1$ .

$\frac{3}{8}$