Precalculus Examples

$\log_{3} (4 a^{7})$

Step 1

Rewrite $\log_{3} (4 a^{7})$ as $\log_{3} (4) + \log_{3} (a^{7})$ .

$\log_{3} (4) + \log_{3} (a^{7})$

Step 2

Expand $\log_{3} (a^{7})$ by moving $7$ outside the logarithm.

$\log_{3} (4) + 7 \log_{3} (a)$

Step 3

Simplify each term.

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Step 3.1

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

$\log_{3} (2^{2}) + 7 \log_{3} (a)$

Step 3.2

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

$2 \log_{3} (2) + 7 \log_{3} (a)$