Precalculus Examples

$\ln (\frac{x^{3} y^{5}}{z^{8}})$

Step 1

Rewrite $\ln (\frac{x^{3} y^{5}}{z^{8}})$ as $\ln (x^{3} y^{5}) - \ln (z^{8})$ .

$\ln (x^{3} y^{5}) - \ln (z^{8})$

Step 2

Expand $\ln (z^{8})$ by moving $8$ outside the logarithm.

$\ln (x^{3} y^{5}) - (8 \ln (z))$

Step 3

Multiply $8$ by $- 1$ .

$\ln (x^{3} y^{5}) - 8 \ln (z)$

Step 4

Rewrite $\ln (x^{3} y^{5})$ as $\ln (x^{3}) + \ln (y^{5})$ .

$\ln (x^{3}) + \ln (y^{5}) - 8 \ln (z)$

Step 5

Expand $\ln (x^{3})$ by moving $3$ outside the logarithm.

$3 \ln (x) + \ln (y^{5}) - 8 \ln (z)$

Step 6

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

$3 \ln (x) + 5 \ln (y) - 8 \ln (z)$