Precalculus Examples

$\ln (\frac{e^{3}}{x^{4}})$

Step 1

Rewrite $\ln (\frac{e^{3}}{x^{4}})$ as $\ln (e^{3}) - \ln (x^{4})$ .

$\ln (e^{3}) - \ln (x^{4})$

Step 2

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

$3 \ln (e) - \ln (x^{4})$

Step 3

Expand $\ln (x^{4})$ by moving $4$ outside the logarithm.

$3 \ln (e) - (4 \ln (x))$

Step 4

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

$3 \cdot 1 - (4 \ln (x))$

Step 5

Multiply $3$ by $1$ .

$3 - (4 \ln (x))$

Step 6

Multiply $4$ by $- 1$ .

$3 - 4 \ln (x)$