Evaluate 8 natural log of e^2- natural log of e^5

$8 \ln (e^{2}) - \ln (e^{5})$

Step 1

Simplify each term.

Use logarithm rules to move $2$ out of the exponent.

$8 (2 \ln (e)) - \ln (e^{5})$

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

$8 (2 \cdot 1) - \ln (e^{5})$

Multiply $2$ by $1$ .

$8 \cdot 2 - \ln (e^{5})$

Multiply $8$ by $2$ .

$16 - \ln (e^{5})$

Use logarithm rules to move $5$ out of the exponent.

$16 - (5 \ln (e))$

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

$16 - (5 \cdot 1)$

Multiply $5$ by $1$ .

$16 - 1 \cdot 5$

Multiply $- 1$ by $5$ .

$16 - 5$

Step 2

Subtract $5$ from $16$ .

$11$