Precalculus Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

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

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

Step 5

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

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