Precalculus Examples

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

Step 1

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

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

Step 2

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

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

Step 3

Logarithm base $3$ of $3$ is $1$ .

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

Step 4

Simplify each term.

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Step 4.1

Apply the distributive property.

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

Step 4.2

Multiply $- 1$ by $1$ .

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