Precalculus Examples

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

Step 1

Multiply the exponents in ${(e^{x})}^{2}$ .

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Step 1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Step 1.2

Move $2$ to the left of $x$ .

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

Step 2

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

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

Step 3

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

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

Step 4

Multiply $2$ by $1$ .

$2 x + x^{2}$