Precalculus Examples

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

Step 1

Simplify each term.

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Step 1.1

Use logarithm rules to move $x^{2} + 2$ out of the exponent.

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

Step 1.2

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

$3 - ((x^{2} + 2) \cdot 1)$

Step 1.3

Multiply $x^{2} + 2$ by $1$ .

$3 - (x^{2} + 2)$

Step 1.4

Apply the distributive property.

$3 - x^{2} - 1 \cdot 2$

Step 1.5

Multiply $- 1$ by $2$ .

$3 - x^{2} - 2$

Step 2

Subtract $2$ from $3$ .

$- x^{2} + 1$