Expand the Logarithmic Expression

$\log_{3} (4 x^{3})$

Step 1

Rewrite $\log_{3} (4 x^{3})$ as $\log_{3} (4) + \log_{3} (x^{3})$ .

$\log_{3} (4) + \log_{3} (x^{3})$

Step 2

Expand $\log_{3} (x^{3})$ by moving $3$ outside the logarithm.

$\log_{3} (4) + 3 \log_{3} (x)$

Step 3

Simplify each term.

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Step 3.1

Rewrite $\log_{3} (4)$ as $\log_{3} (2^{2})$ .

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

Step 3.2

Expand $\log_{3} (2^{2})$ by moving $2$ outside the logarithm.

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

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Exponential and Logarithmic Functions

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$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$