Precalculus Examples

$\log_{3} (4 x^{5})$

Step 1

Rewrite $\log_{3} (4 x^{5})$ as $\log_{3} (4) + \log_{3} (x^{5})$ .

$\log_{3} (4) + \log_{3} (x^{5})$

Step 2

Expand $\log_{3} (x^{5})$ by moving $5$ outside the logarithm.

$\log_{3} (4) + 5 \log_{3} (x)$

Step 3

Simplify each term.

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Step 3.1

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

$\log_{3} (2^{2}) + 5 \log_{3} (x)$

Step 3.2

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

$2 \log_{3} (2) + 5 \log_{3} (x)$