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

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

Step 1

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

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

Step 2

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

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

Step 3

The natural logarithm of $e$ is $1$ .

$\frac{3}{4} \cdot 1$

Step 4

Multiply $\frac{3}{4}$ by $1$ .

$\frac{3}{4}$