Evaluate 3 natural log of e^4- natural log of e^8

$3 \ln (e^{4}) - \ln (e^{8})$

Step 1

Simplify each term.

Use logarithm rules to move $4$ out of the exponent.

$3 (4 \ln (e)) - \ln (e^{8})$

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

$3 (4 \cdot 1) - \ln (e^{8})$

Multiply $4$ by $1$ .

$3 \cdot 4 - \ln (e^{8})$

Multiply $3$ by $4$ .

$12 - \ln (e^{8})$

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

$12 - (8 \ln (e))$

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

$12 - (8 \cdot 1)$

Multiply $8$ by $1$ .

$12 - 1 \cdot 8$

Multiply $- 1$ by $8$ .

$12 - 8$

Step 2

Subtract $8$ from $12$ .

$4$