Precalculus Examples

$\ln (\frac{a^{2} b^{3}}{\sqrt{c}})$

Step 1

Rewrite $\ln (\frac{a^{2} b^{3}}{\sqrt{c}})$ as $\ln (a^{2} b^{3}) - \ln (\sqrt{c})$ .

$\ln (a^{2} b^{3}) - \ln (\sqrt{c})$

Step 2

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

$\ln (a^{2} b^{3}) - \ln (c^{\frac{1}{2}})$

Step 3

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

$\ln (a^{2} b^{3}) - (\frac{1}{2} \ln (c))$

Step 4

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

$\ln (a^{2} b^{3}) - \frac{\ln (c)}{2}$

Step 5

Rewrite $\ln (a^{2} b^{3})$ as $\ln (a^{2}) + \ln (b^{3})$ .

$\ln (a^{2}) + \ln (b^{3}) - \frac{\ln (c)}{2}$

Step 6

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

$2 \ln (a) + \ln (b^{3}) - \frac{\ln (c)}{2}$

Step 7

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

$2 \ln (a) + 3 \ln (b) - \frac{\ln (c)}{2}$