Precalculus Examples

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

Step 1

Simplify $3 \ln (x^{2})$ by moving $3$ inside the logarithm.

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

Step 2

Exponentiation and log are inverse functions.

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

Step 3

Multiply the exponents in ${(x^{2})}^{3}$ .

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Step 3.1

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

$x^{2 \cdot 3}$

Step 3.2

Multiply $2$ by $3$ .

$x^{6}$