Precalculus Examples

$\log_{9} (25) - \log_{9} (75)$

Step 1

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

$\log_{9} (\frac{25}{75})$

Step 2

Cancel the common factor of $25$ and $75$ .

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Step 2.1

Factor $25$ out of $25$ .

$\log_{9} (\frac{25 (1)}{75})$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $25$ out of $75$ .

$\log_{9} (\frac{25 \cdot 1}{25 \cdot 3})$

Step 2.2.2

Cancel the common factor.

$\log_{9} (\frac{25 \cdot 1}{25 \cdot 3})$

Step 2.2.3

Rewrite the expression.

$\log_{9} (\frac{1}{3})$

Step 3

Logarithm base $9$ of $\frac{1}{3}$ is $- \frac{1}{2}$ .

$- \frac{1}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{2}$

Decimal Form:

$- 0.5$