Expand the Logarithmic Expression natural log of fifth root of x^7

$\ln (\sqrt[5]{x^{7}})$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[5]{x^{7}}$ as $x^{\frac{7}{5}}$ .

$\ln (x^{\frac{7}{5}})$

Step 2

Expand $\ln (x^{\frac{7}{5}})$ by moving $\frac{7}{5}$ outside the logarithm.

$\frac{7}{5} \ln (x)$

Step 3

Combine $\frac{7}{5}$ and $\ln (x)$ .

$\frac{7 \ln (x)}{5}$