Precalculus Examples

$\ln (\frac{x^{2} - 1}{x^{7}})$

Step 1

Rewrite $\ln (\frac{x^{2} - 1}{x^{7}})$ as $\ln (x^{2} - 1) - \ln (x^{7})$ .

$\ln (x^{2} - 1) - \ln (x^{7})$

Step 2

Expand $\ln (x^{7})$ by moving $7$ outside the logarithm.

$\ln (x^{2} - 1) - (7 \ln (x))$

Step 3

Multiply $7$ by $- 1$ .

$\ln (x^{2} - 1) - 7 \ln (x)$