Precalculus Examples

$\log_{3} ({(\frac{11^{4}}{5})}^{2})$

Step 1

Expand $\log_{3} ({(\frac{11^{4}}{5})}^{2})$ by moving $2$ outside the logarithm.

$2 \log_{3} (\frac{11^{4}}{5})$

Step 2

Raise $11$ to the power of $4$ .

$2 \log_{3} (\frac{14641}{5})$

Step 3

Rewrite $\log_{3} (\frac{14641}{5})$ as $\log_{3} (14641) - \log_{3} (5)$ .

$2 (\log_{3} (14641) - \log_{3} (5))$

Step 4

Simplify each term.

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Step 4.1

Rewrite $\log_{3} (14641)$ as $\log_{3} (11^{4})$ .

$2 (\log_{3} (11^{4}) - \log_{3} (5))$

Step 4.2

Expand $\log_{3} (11^{4})$ by moving $4$ outside the logarithm.

$2 (4 \log_{3} (11) - \log_{3} (5))$

Step 5

Apply the distributive property.

$2 (4 \log_{3} (11)) + 2 (- \log_{3} (5))$

Step 6

Multiply $4$ by $2$ .

$8 \log_{3} (11) + 2 (- \log_{3} (5))$

Step 7

Multiply $- 1$ by $2$ .

$8 \log_{3} (11) - 2 \log_{3} (5)$