Expand the Logarithmic Expression natural log of sixth root of x

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

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

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

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

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

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

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