Precalculus Examples

$\ln (\frac{e^{6}}{14})$

Step 1

Rewrite $\ln (\frac{e^{6}}{14})$ as $\ln (e^{6}) - \ln (14)$ .

$\ln (e^{6}) - \ln (14)$

Step 2

Expand $\ln (e^{6})$ by moving $6$ outside the logarithm.

$6 \ln (e) - \ln (14)$

Step 3

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

$6 \cdot 1 - \ln (14)$

Step 4

Multiply $6$ by $1$ .

$6 - \ln (14)$

Step 5

Rewrite $\ln (14)$ as $\ln (2 (7))$ .

$6 - \ln (2 (7))$

Step 6

Rewrite $\ln (2 (7))$ as $\ln (2) + \ln (7)$ .

$6 - (\ln (2) + \ln (7))$

Step 7

Apply the distributive property.

$6 - \ln (2) - \ln (7)$