Precalculus Examples

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

Step 1

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

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

Step 2

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

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

Step 3

Divide $2$ by $2$ .

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

Step 4

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

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

Step 5

Multiply $\ln (c)$ by $1$ .

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

Step 6

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

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

Step 7

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

$\ln (a) + 3 \ln (b) - \ln (c)$