Precalculus Examples

$\ln (\frac{3 x^{2}}{{(x + 1)}^{10}})$

Step 1

Rewrite $\ln (\frac{3 x^{2}}{{(x + 1)}^{10}})$ as $\ln (3 x^{2}) - \ln ({(x + 1)}^{10})$ .

$\ln (3 x^{2}) - \ln ({(x + 1)}^{10})$

Step 2

Expand $\ln ({(x + 1)}^{10})$ by moving $10$ outside the logarithm.

$\ln (3 x^{2}) - (10 \ln (x + 1))$

Step 3

Multiply $10$ by $- 1$ .

$\ln (3 x^{2}) - 10 \ln (x + 1)$

Step 4

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

$\ln (3) + \ln (x^{2}) - 10 \ln (x + 1)$

Step 5

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

$\ln (3) + 2 \ln (x) - 10 \ln (x + 1)$