Precalculus Examples

$\ln (\sqrt[6]{\ln (y)})$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[6]{\ln (y)}$ as ${\ln (y)}^{\frac{1}{6}}$ .

$\ln ({\ln (y)}^{\frac{1}{6}})$

Step 2

Expand $\ln ({\ln (y)}^{\frac{1}{6}})$ by moving $\frac{1}{6}$ outside the logarithm.

$\frac{1}{6} \ln (\ln (y))$

Step 3

Combine $\frac{1}{6}$ and $\ln (\ln (y))$ .

$\frac{\ln (\ln (y))}{6}$