Precalculus Examples

$3 \ln (e^{9}) - \ln (e^{9})$

Step 1

Expand $\ln (e^{9})$ by moving $9$ outside the logarithm.

$3 (9 \ln (e)) - \ln (e^{9})$

Step 2

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

$3 (9 \cdot 1) - \ln (e^{9})$

Step 3

Multiply $9$ by $1$ .

$3 \cdot 9 - \ln (e^{9})$

Step 4

Expand $\ln (e^{9})$ by moving $9$ outside the logarithm.

$3 \cdot 9 - (9 \ln (e))$

Step 5

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

$3 \cdot 9 - (9 \cdot 1)$

Step 6

Multiply $9$ by $1$ .

$3 \cdot 9 - 1 \cdot 9$

Step 7

Simplify each term.

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Step 7.1

Multiply $3$ by $9$ .

$27 - 1 \cdot 9$

Step 7.2

Multiply $- 1$ by $9$ .

$27 - 9$

Step 8

Subtract $9$ from $27$ .

$18$