Expand the Logarithmic Expression natural log of (e^5)/9

$\ln (\frac{e^{5}}{9})$

Step 1

Rewrite $\ln (\frac{e^{5}}{9})$ as $\ln (e^{5}) - \ln (9)$ .

$\ln (e^{5}) - \ln (9)$

Step 2

Expand $\ln (e^{5})$ by moving $5$ outside the logarithm.

$5 \ln (e) - \ln (9)$

Step 3

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

$5 \cdot 1 - \ln (9)$

Step 4

Multiply $5$ by $1$ .

$5 - \ln (9)$

Step 5

Rewrite $\ln (9)$ as $\ln (3^{2})$ .

$5 - \ln (3^{2})$

Step 6

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

$5 - (2 \ln (3))$

Step 7

Multiply $2$ by $- 1$ .

$5 - 2 \ln (3)$