Precalculus Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

Multiply $2$ by $1$ .

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

Step 1.4

Simplify $2 \ln (x)$ by moving $2$ inside the logarithm.

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

Step 1.5

Exponentiation and log are inverse functions.

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

Step 1.6

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

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

Step 1.7

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

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

Step 1.8

Multiply $2$ by $1$ .

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

Step 1.9

Multiply $- 1$ by $2$ .

$x^{2} + x^{2} - 2$

Step 2

Add $x^{2}$ and $x^{2}$ .

$2 x^{2} - 2$