Expand the Logarithmic Expression natural log of fourth root of x^3

$\ln (\sqrt[4]{x^{3}})$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{x^{3}}$ as $x^{\frac{3}{4}}$ .

$\ln (x^{\frac{3}{4}})$

Step 2

Expand $\ln (x^{\frac{3}{4}})$ by moving $\frac{3}{4}$ outside the logarithm.

$\frac{3}{4} \ln (x)$

Step 3

Combine $\frac{3}{4}$ and $\ln (x)$ .

$\frac{3 \ln (x)}{4}$