Expand the Logarithmic Expression natural log of ninth root of x

$\ln (\sqrt[9]{x})$

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[9]{x}$ as $x^{\frac{1}{9}}$ .

$\ln (x^{\frac{1}{9}})$

Expand $\ln (x^{\frac{1}{9}})$ by moving $\frac{1}{9}$ outside the logarithm.

$\frac{1}{9} \ln (x)$

Combine $\frac{1}{9}$ and $\ln (x)$ .

$\frac{\ln (x)}{9}$