Precalculus Examples

$\log_{9} (x^{4}) - \log_{9} (7 x^{5})$

Step 1

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

$\log_{9} (\frac{x^{4}}{7 x^{5}})$

Step 2

Cancel the common factor of $x^{4}$ and $x^{5}$ .

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Step 2.1

Multiply by $1$ .

$\log_{9} (\frac{x^{4} \cdot 1}{7 x^{5}})$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $x^{4}$ out of $7 x^{5}$ .

$\log_{9} (\frac{x^{4} \cdot 1}{x^{4} (7 x)})$

Step 2.2.2

Cancel the common factor.

$\log_{9} (\frac{x^{4} \cdot 1}{x^{4} (7 x)})$

Step 2.2.3

Rewrite the expression.

$\log_{9} (\frac{1}{7 x})$