Precalculus Examples

$\ln (\frac{x^{2} y}{z^{7}})$

Step 1

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

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

Step 2

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

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

Step 3

Multiply $7$ by $- 1$ .

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

Step 4

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

$\ln (x^{2}) + \ln (y) - 7 \ln (z)$

Step 5

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

$2 \ln (x) + \ln (y) - 7 \ln (z)$