Precalculus Examples

$\ln (\frac{{(x + 1)}^{2}}{{(x - 1)}^{4}})$

Step 1

Rewrite $\ln (\frac{{(x + 1)}^{2}}{{(x - 1)}^{4}})$ as $\ln ({(x + 1)}^{2}) - \ln ({(x - 1)}^{4})$ .

$\ln ({(x + 1)}^{2}) - \ln ({(x - 1)}^{4})$

Step 2

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

$2 \ln (x + 1) - \ln ({(x - 1)}^{4})$

Step 3

Expand $\ln ({(x - 1)}^{4})$ by moving $4$ outside the logarithm.

$2 \ln (x + 1) - (4 \ln (x - 1))$

Step 4

Multiply $4$ by $- 1$ .

$2 \ln (x + 1) - 4 \ln (x - 1)$