Precalculus Examples

$\ln (\frac{e^{3}}{8})$

Step 1

Rewrite $\ln (\frac{e^{3}}{8})$ as $\ln (e^{3}) - \ln (8)$ .

$\ln (e^{3}) - \ln (8)$

Step 2

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

$3 \ln (e) - \ln (8)$

Step 3

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

$3 \cdot 1 - \ln (8)$

Step 4

Multiply $3$ by $1$ .

$3 - \ln (8)$

Step 5

Rewrite $\ln (8)$ as $\ln (2^{3})$ .

$3 - \ln (2^{3})$

Step 6

Expand $\ln (2^{3})$ by moving $3$ outside the logarithm.

$3 - (3 \ln (2))$

Step 7

Multiply $3$ by $- 1$ .

$3 - 3 \ln (2)$