Precalculus Examples

$\ln (x^{8} \sqrt[3]{y^{4}})$

Step 1

Rewrite $\ln (x^{8} \sqrt[3]{y^{4}})$ as $\ln (x^{8}) + \ln (\sqrt[3]{y^{4}})$ .

$\ln (x^{8}) + \ln (\sqrt[3]{y^{4}})$

Step 2

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

$\ln (x^{8}) + \ln (y^{\frac{4}{3}})$

Step 3

Expand $\ln (x^{8})$ by moving $8$ outside the logarithm.

$8 \ln (x) + \ln (y^{\frac{4}{3}})$

Step 4

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

$8 \ln (x) + \frac{4}{3} \ln (y)$

Step 5

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

$8 \ln (x) + \frac{4 \ln (y)}{3}$