Precalculus Examples

$11 \log_{9} (x - 3) - 5 \log_{9} (2 x)$

Step 1

Simplify each term.

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Step 1.1

Simplify $11 \log_{9} (x - 3)$ by moving $11$ inside the logarithm.

$\log_{9} ({(x - 3)}^{11}) - 5 \log_{9} (2 x)$

Step 1.2

Simplify $- 5 \log_{9} (2 x)$ by moving $5$ inside the logarithm.

$\log_{9} ({(x - 3)}^{11}) - \log_{9} ({(2 x)}^{5})$

Step 1.3

Apply the product rule to $2 x$ .

$\log_{9} ({(x - 3)}^{11}) - \log_{9} (2^{5} x^{5})$

Step 1.4

Raise $2$ to the power of $5$ .

$\log_{9} ({(x - 3)}^{11}) - \log_{9} (32 x^{5})$

Step 2

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

$\log_{9} (\frac{{(x - 3)}^{11}}{32 x^{5}})$