Expand the Logarithmic Expression natural log of cube root of 4

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

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{4}$ as $4^{\frac{1}{3}}$ .

$\ln (4^{\frac{1}{3}})$

Step 2

Expand $\ln (4^{\frac{1}{3}})$ by moving $\frac{1}{3}$ outside the logarithm.

$\frac{1}{3} \ln (4)$

Step 3

Rewrite $\ln (4)$ as $\ln (2^{2})$ .

$\frac{1}{3} \ln (2^{2})$

Step 4

Expand $\ln (2^{2})$ by moving $2$ outside the logarithm.

$\frac{1}{3} (2 \ln (2))$

Step 5

Multiply $\frac{1}{3} (2 \ln (2))$ .

Combine $2$ and $\frac{1}{3}$ .

$\frac{2}{3} \ln (2)$

Combine $\frac{2}{3}$ and $\ln (2)$ .

$\frac{2 \ln (2)}{3}$