Precalculus Examples

$\log_{3} ({(\frac{4 x}{y})}^{2})$

Step 1

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

$2 \log_{3} (\frac{4 x}{y})$

Step 2

Rewrite $\log_{3} (\frac{4 x}{y})$ as $\log_{3} (4 x) - \log_{3} (y)$ .

$2 (\log_{3} (4 x) - \log_{3} (y))$

Step 3

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

$2 (\log_{3} (4) + \log_{3} (x) - \log_{3} (y))$

Step 4

Simplify each term.

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Step 4.1

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

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

Step 4.2

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

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

Step 5

Apply the distributive property.

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

Step 6

Simplify.

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Step 6.1

Multiply $2$ by $2$ .

$4 \log_{3} (2) + 2 \log_{3} (x) + 2 (- \log_{3} (y))$

Step 6.2

Multiply $- 1$ by $2$ .

$4 \log_{3} (2) + 2 \log_{3} (x) - 2 \log_{3} (y)$