Precalculus Examples

$\ln (\frac{e^{4}}{12})$

Step 1

Rewrite $\ln (\frac{e^{4}}{12})$ as $\ln (e^{4}) - \ln (12)$ .

$\ln (e^{4}) - \ln (12)$

Step 2

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

$4 \ln (e) - \ln (12)$

Step 3

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

$4 \cdot 1 - \ln (12)$

Step 4

Multiply $4$ by $1$ .

$4 - \ln (12)$

Step 5

Rewrite $\ln (12)$ as $\ln (2^{2} \cdot 3)$ .

$4 - \ln (2^{2} \cdot 3)$

Step 6

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

$4 - (\ln (2^{2}) + \ln (3))$

Step 7

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

$4 - (2 \ln (2) + \ln (3))$

Step 8

Apply the distributive property.

$4 - (2 \ln (2)) - \ln (3)$

Step 9

Multiply $2$ by $- 1$ .

$4 - 2 \ln (2) - \ln (3)$