Precalculus Examples

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

Step 1

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

$\ln (x y^{2}) - \ln (\sqrt{z})$

Step 2

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{z}$ as $z^{\frac{1}{2}}$ .

$\ln (x y^{2}) - \ln (z^{\frac{1}{2}})$

Step 3

Expand $\ln (z^{\frac{1}{2}})$ by moving $\frac{1}{2}$ outside the logarithm.

$\ln (x y^{2}) - (\frac{1}{2} \ln (z))$

Step 4

Combine $\frac{1}{2}$ and $\ln (z)$ .

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

Step 5

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

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

Step 6

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

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