Precalculus Examples

$\log_{3} (9) - \log_{3} (15) + \log_{3} (15)$

Step 1

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\log_{3} (\frac{9}{15}) + \log_{3} (15)$

Step 2

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

$\log_{3} (\frac{9}{15} \cdot 15)$

Step 3

Cancel the common factor of $15$ .

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Step 3.1

Cancel the common factor.

$\log_{3} (\frac{9}{15} \cdot 15)$

Step 3.2

Rewrite the expression.

$\log_{3} (9)$

Step 4

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

$2$