Expand the Logarithmic Expression natural log of 12 root of x

$\ln (\sqrt[12]{x})$

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[12]{x}$ as $x^{\frac{1}{12}}$ .

$\ln (x^{\frac{1}{12}})$

Expand $\ln (x^{\frac{1}{12}})$ by moving $\frac{1}{12}$ outside the logarithm.

$\frac{1}{12} \ln (x)$

Combine $\frac{1}{12}$ and $\ln (x)$ .

$\frac{\ln (x)}{12}$