Expand the Logarithmic Expression natural log of 13 root of x

$\ln (\sqrt[13]{x})$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[13]{x}$ as $x^{\frac{1}{13}}$ .

$\ln (x^{\frac{1}{13}})$

Step 2

Expand $\ln (x^{\frac{1}{13}})$ by moving $\frac{1}{13}$ outside the logarithm.

$\frac{1}{13} \ln (x)$

Step 3

Combine $\frac{1}{13}$ and $\ln (x)$ .

$\frac{\ln (x)}{13}$