Precalculus Examples

$\log_{3} (108) + \log_{3} (\frac{3}{4})$

Step 1

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

$\log_{3} (108 (\frac{3}{4}))$

Step 2

Cancel the common factor of $4$ .

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Step 2.1

Factor $4$ out of $108$ .

$\log_{3} (4 (27) \frac{3}{4})$

Step 2.2

Cancel the common factor.

$\log_{3} (4 \cdot 27 \frac{3}{4})$

Step 2.3

Rewrite the expression.

$\log_{3} (27 \cdot 3)$

Step 3

Simplify the expression.

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Step 3.1

Multiply $27$ by $3$ .

$\log_{3} (81)$

Step 3.2

Logarithm base $3$ of $81$ is $4$ .

$4$