Evaluate 7 natural log of e^3- natural log of e^8

$7 \ln (e^{3}) - \ln (e^{8})$

Simplify each term.

Use logarithm rules to move $3$ out of the exponent.

$7 (3 \ln (e)) - \ln (e^{8})$

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

$7 (3 \cdot 1) - \ln (e^{8})$

Multiply $3$ by $1$ .

$7 \cdot 3 - \ln (e^{8})$

Multiply $7$ by $3$ .

$21 - \ln (e^{8})$

Use logarithm rules to move $8$ out of the exponent.

$21 - (8 \ln (e))$

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

$21 - (8 \cdot 1)$

Multiply $8$ by $1$ .

$21 - 1 \cdot 8$

Multiply $- 1$ by $8$ .

$21 - 8$

Subtract $8$ from $21$ .

$13$