Precalculus Examples

$\ln (\sqrt[11]{e})$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[11]{e}$ as $e^{\frac{1}{11}}$ .

$\ln (e^{\frac{1}{11}})$

Step 2

Expand $\ln (e^{\frac{1}{11}})$ by moving $\frac{1}{11}$ outside the logarithm.

$\frac{1}{11} \ln (e)$

Step 3

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

$\frac{1}{11} \cdot 1$

Step 4

Multiply $\frac{1}{11}$ by $1$ .

$\frac{1}{11}$