Precalculus Examples

${(3^{\ln (x^{2})})}^{\frac{1}{\ln (3)}}$

Step 1

Multiply the exponents in ${(3^{\ln (x^{2})})}^{\frac{1}{\ln (3)}}$ .

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Step 1.1

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

$3^{\ln (x^{2}) \frac{1}{\ln (3)}}$

Step 1.2

Combine $\ln (x^{2})$ and $\frac{1}{\ln (3)}$ .

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

Step 2

Use the change of base rule $\frac{\log_{b} (x)}{\log_{b} (a)} = \log_{a} (x)$ .

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

Step 3

Exponentiation and log are inverse functions.

$x^{2}$