Algebra Examples

$\ln (\frac{w^{3}}{\sqrt{z}})$

Step 1

Rewrite $\ln (\frac{w^{3}}{\sqrt{z}})$ as $\ln (w^{3}) - \ln (\sqrt{z})$ .

$\ln (w^{3}) - \ln (\sqrt{z})$

Step 2

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

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

Step 3

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

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

Step 4

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

$3 \ln (w) - (\frac{1}{2} \ln (z))$

Step 5

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

$3 \ln (w) - \frac{\ln (z)}{2}$