Precalculus Examples

$\ln (x^{5} y^{7} z)$

Step 1

Rewrite $\ln (x^{5} y^{7} z)$ as $\ln (x^{5} y^{7}) + \ln (z)$ .

$\ln (x^{5} y^{7}) + \ln (z)$

Step 2

Rewrite $\ln (x^{5} y^{7})$ as $\ln (x^{5}) + \ln (y^{7})$ .

$\ln (x^{5}) + \ln (y^{7}) + \ln (z)$

Step 3

Expand $\ln (x^{5})$ by moving $5$ outside the logarithm.

$5 \ln (x) + \ln (y^{7}) + \ln (z)$

Step 4

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

$5 \ln (x) + 7 \ln (y) + \ln (z)$