Precalculus Examples

$2 \ln (e^{6}) - \ln (e^{5})$

Step 1

Simplify each term.

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Step 1.1

Use logarithm rules to move $6$ out of the exponent.

$2 (6 \ln (e)) - \ln (e^{5})$

Step 1.2

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

$2 (6 \cdot 1) - \ln (e^{5})$

Step 1.3

Multiply $6$ by $1$ .

$2 \cdot 6 - \ln (e^{5})$

Step 1.4

Multiply $2$ by $6$ .

$12 - \ln (e^{5})$

Step 1.5

Use logarithm rules to move $5$ out of the exponent.

$12 - (5 \ln (e))$

Step 1.6

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

$12 - (5 \cdot 1)$

Step 1.7

Multiply $5$ by $1$ .

$12 - 1 \cdot 5$

Step 1.8

Multiply $- 1$ by $5$ .

$12 - 5$

Step 2

Subtract $5$ from $12$ .

$7$