Precalculus Examples

$3 \ln (e) + 4 \ln (e^{2}) - 2 \ln (e)$

Step 1

Simplify each term.

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Step 1.1

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

$3 \cdot 1 + 4 \ln (e^{2}) - 2 \ln (e)$

Step 1.2

Multiply $3$ by $1$ .

$3 + 4 \ln (e^{2}) - 2 \ln (e)$

Step 1.3

Use logarithm rules to move $2$ out of the exponent.

$3 + 4 (2 \ln (e)) - 2 \ln (e)$

Step 1.4

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

$3 + 4 (2 \cdot 1) - 2 \ln (e)$

Step 1.5

Multiply $2$ by $1$ .

$3 + 4 \cdot 2 - 2 \ln (e)$

Step 1.6

Multiply $4$ by $2$ .

$3 + 8 - 2 \ln (e)$

Step 1.7

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

$3 + 8 - 2 \cdot 1$

Step 1.8

Multiply $- 2$ by $1$ .

$3 + 8 - 2$

$3 + 8 - 2$

Step 2

Simplify by adding and subtracting.

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Step 2.1

Add $3$ and $8$ .

$11 - 2$

Step 2.2

Subtract $2$ from $11$ .

$9$

$9$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$