Precalculus Examples

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

Step 1

Apply the distributive property.

$\log_{9} (x^{2}) x + \log_{9} (x^{2}) \cdot - 2$

Step 2

Multiply $\log_{9} (x^{2}) \cdot - 2$ .

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Step 2.1

Reorder $\log_{9} (x^{2})$ and $- 2$ .

$\log_{9} (x^{2}) x - 2 \cdot \log_{9} (x^{2})$

Step 2.2

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

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

Step 3

Multiply the exponents in ${(x^{2})}^{2}$ .

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Step 3.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\log_{9} (x^{2}) x - \log_{9} (x^{2 \cdot 2})$

Step 3.2

Multiply $2$ by $2$ .

$\log_{9} (x^{2}) x - \log_{9} (x^{4})$

Step 4

Reorder factors in $\log_{9} (x^{2}) x - \log_{9} (x^{4})$ .

$x \log_{9} (x^{2}) - \log_{9} (x^{4})$