Calculus Examples

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

Step 1

Rewrite $\ln (e^{- 8} e^{4})$ as $\ln (e^{- 8}) + \ln (e^{4})$ .

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

Step 2

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

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

Step 3

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

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

Step 4

Multiply $- 8$ by $1$ .

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

Step 5

Simplify each term.

Tap for more steps...

Step 5.1

Expand $\ln (e^{4})$ by moving $4$ outside the logarithm.

$- 8 + 4 \ln (e)$

Step 5.2

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

$- 8 + 4 \cdot 1$

Step 5.3

Multiply $4$ by $1$ .

$- 8 + 4$

Step 6

Add $- 8$ and $4$ .

$- 4$