Precalculus Examples

$\ln (e^{2} p) - \ln (q^{3})$

Step 1

Rewrite $\ln (e^{2} p)$ as $\ln (e^{2}) + \ln (p)$ .

$\ln (e^{2}) + \ln (p) - \ln (q^{3})$

Step 2

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

$2 \ln (e) + \ln (p) - \ln (q^{3})$

Step 3

The natural logarithm of $e$ is $1$ .

$2 \cdot 1 + \ln (p) - \ln (q^{3})$

Step 4

Multiply $2$ by $1$ .

$2 + \ln (p) - \ln (q^{3})$

Step 5

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

$2 + \ln (p) - (3 \ln (q))$

Step 6

Multiply $3$ by $- 1$ .

$2 + \ln (p) - 3 \ln (q)$