Precalculus Examples

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

Step 1

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

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

Step 2

Exponentiation and log are inverse functions.

${(2 \sqrt{x})}^{2}$

Step 3

Simplify the expression.

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Step 3.1

Apply the product rule to $2 \sqrt{x}$ .

$2^{2} {\sqrt{x}}^{2}$

Step 3.2

Raise $2$ to the power of $2$ .

$4 {\sqrt{x}}^{2}$

Step 4

Rewrite ${\sqrt{x}}^{2}$ as $x$ .

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Step 4.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x}$ as $x^{\frac{1}{2}}$ .

$4 {(x^{\frac{1}{2}})}^{2}$

Step 4.2

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

$4 x^{\frac{1}{2} \cdot 2}$

Step 4.3

Combine $\frac{1}{2}$ and $2$ .

$4 x^{\frac{2}{2}}$

Step 4.4

Cancel the common factor of $2$ .

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Step 4.4.1

Cancel the common factor.

$4 x^{\frac{2}{2}}$

Step 4.4.2

Rewrite the expression.

$4 x^{1}$

Step 4.5

Simplify.

$4 x$