Precalculus Examples

$\ln (x^{\frac{2}{3}} y^{\frac{4}{3}})$

Step 1

Rewrite $\ln (x^{\frac{2}{3}} y^{\frac{4}{3}})$ as $\ln (x^{\frac{2}{3}}) + \ln (y^{\frac{4}{3}})$ .

$\ln (x^{\frac{2}{3}}) + \ln (y^{\frac{4}{3}})$

Step 2

Expand $\ln (x^{\frac{2}{3}})$ by moving $\frac{2}{3}$ outside the logarithm.

$\frac{2}{3} \ln (x) + \ln (y^{\frac{4}{3}})$

Step 3

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

$\frac{2}{3} \ln (x) + \frac{4}{3} \ln (y)$

Step 4

Simplify each term.

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Step 4.1

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

$\frac{2 \ln (x)}{3} + \frac{4}{3} \ln (y)$

Step 4.2

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

$\frac{2 \ln (x)}{3} + \frac{4 \ln (y)}{3}$