Precalculus Examples

$\log_{3} (\frac{{(x - 2)}^{3}}{9 y})$

Step 1

Rewrite $\log_{3} (\frac{{(x - 2)}^{3}}{9 y})$ as $\log_{3} ({(x - 2)}^{3}) - \log_{3} (9 y)$ .

$\log_{3} ({(x - 2)}^{3}) - \log_{3} (9 y)$

Step 2

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

$3 \log_{3} (x - 2) - \log_{3} (9 y)$

Step 3

Rewrite $\log_{3} (9 y)$ as $\log_{3} (9) + \log_{3} (y)$ .

$3 \log_{3} (x - 2) - (\log_{3} (9) + \log_{3} (y))$

Step 4

Logarithm base $3$ of $9$ is $2$ .

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

Step 5

Simplify each term.

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Step 5.1

Apply the distributive property.

$3 \log_{3} (x - 2) - 1 \cdot 2 - \log_{3} (y)$

Step 5.2

Multiply $- 1$ by $2$ .

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