Precalculus Examples

$\ln (\frac{11 x^{2}}{y^{5}})$

Step 1

Rewrite $\ln (\frac{11 x^{2}}{y^{5}})$ as $\ln (11 x^{2}) - \ln (y^{5})$ .

$\ln (11 x^{2}) - \ln (y^{5})$

Step 2

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

$\ln (11 x^{2}) - (5 \ln (y))$

Step 3

Multiply $5$ by $- 1$ .

$\ln (11 x^{2}) - 5 \ln (y)$

Step 4

Rewrite $\ln (11 x^{2})$ as $\ln (11) + \ln (x^{2})$ .

$\ln (11) + \ln (x^{2}) - 5 \ln (y)$

Step 5

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

$\ln (11) + 2 \ln (x) - 5 \ln (y)$