Precalculus Examples

$\log_{3} (6 x) + \log_{3} (\frac{1}{12})$

Step 1

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\log_{3} (6 x \frac{1}{12})$

Step 2

Cancel the common factor of $6$ .

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Step 2.1

Factor $6$ out of $6 x$ .

$\log_{3} (6 (x) \frac{1}{12})$

Step 2.2

Factor $6$ out of $12$ .

$\log_{3} (6 (x) \frac{1}{6 (2)})$

Step 2.3

Cancel the common factor.

$\log_{3} (6 x \frac{1}{6 \cdot 2})$

Step 2.4

Rewrite the expression.

$\log_{3} (x \frac{1}{2})$

Step 3

Combine $x$ and $\frac{1}{2}$ .

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