Precalculus Examples

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

Step 1

Simplify $\frac{1}{2} \ln (x)$ by moving $\frac{1}{2}$ inside the logarithm.

$e^{2 \ln (x^{\frac{1}{2}})}$

Step 2

Simplify $2 \ln (x^{\frac{1}{2}})$ by moving $2$ inside the logarithm.

$e^{\ln ({(x^{\frac{1}{2}})}^{2})}$

Step 3

Exponentiation and log are inverse functions.

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

Step 4

Multiply the exponents in ${(x^{\frac{1}{2}})}^{2}$ .

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Step 4.1

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

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

Step 4.2

Cancel the common factor of $2$ .

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Step 4.2.1

Cancel the common factor.

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

Step 4.2.2

Rewrite the expression.

$x^{1}$

Step 5

Simplify.

$x$