Precalculus Examples

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

Step 1

Rewrite $\log_{3} (\frac{5}{x^{2} y})$ as $\log_{3} (5) - \log_{3} (x^{2} y)$ .

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

Step 2

Rewrite $\log_{3} (x^{2} y)$ as $\log_{3} (x^{2}) + \log_{3} (y)$ .

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

Step 3

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

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

Step 4

Simplify each term.

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Step 4.1

Apply the distributive property.

$\log_{3} (5) - (2 \log_{3} (x)) - \log_{3} (y)$

Step 4.2

Multiply $2$ by $- 1$ .

$\log_{3} (5) - 2 \log_{3} (x) - \log_{3} (y)$