Precalculus Examples

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

Step 1

Expand $\ln ({(e)}^{3})$ by moving $3$ outside the logarithm.

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

Step 2

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

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

Step 3

Multiply $3$ by $1$ .

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

Step 4

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

$3 - (7 \ln (e))$

Step 5

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

$3 - (7 \cdot 1)$

Step 6

Multiply $7$ by $1$ .

$3 - 1 \cdot 7$

Step 7

Multiply $- 1$ by $7$ .

$3 - 7$

Step 8

Subtract $7$ from $3$ .

$- 4$