Expand the Logarithmic Expression natural log of seventh root of x

$\ln (\sqrt[7]{x})$

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[7]{x}$ as $x^{\frac{1}{7}}$ .

$\ln (x^{\frac{1}{7}})$

Expand $\ln (x^{\frac{1}{7}})$ by moving $\frac{1}{7}$ outside the logarithm.

$\frac{1}{7} \ln (x)$

Combine $\frac{1}{7}$ and $\ln (x)$ .

$\frac{\ln (x)}{7}$