Trigonometry Examples

$\ln (\frac{1}{e^{7}})$

Step 1

Rewrite $\ln (\frac{1}{e^{7}})$ as $\ln (1) - \ln (e^{7})$ .

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

Step 2

Expand $\ln (e^{7})$ by moving $7$ outside the logarithm.

$\ln (1) - (7 \ln (e))$

Step 3

The natural logarithm of $1$ is $0$ .

$0 - (7 \ln (e))$

Step 4

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

$0 - (7 \cdot 1)$

Step 5

Multiply $7$ by $1$ .

$0 - 1 \cdot 7$

Step 6

Multiply $- 1$ by $7$ .

$0 - 7$

Step 7

Subtract $7$ from $0$ .

$- 7$