Precalculus Examples

$\log_{9} ({(\frac{2^{2}}{5})}^{2})$

Step 1

Expand $\log_{9} ({(\frac{2^{2}}{5})}^{2})$ by moving $2$ outside the logarithm.

$2 \log_{9} (\frac{2^{2}}{5})$

Step 2

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

$2 \log_{9} (\frac{4}{5})$

Step 3

Rewrite $\log_{9} (\frac{4}{5})$ as $\log_{9} (4) - \log_{9} (5)$ .

$2 (\log_{9} (4) - \log_{9} (5))$

Step 4

Simplify each term.

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Step 4.1

Rewrite $\log_{9} (4)$ as $\log_{9} (2^{2})$ .

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

Step 4.2

Expand $\log_{9} (2^{2})$ by moving $2$ outside the logarithm.

$2 (2 \log_{9} (2) - \log_{9} (5))$

Step 5

Apply the distributive property.

$2 (2 \log_{9} (2)) + 2 (- \log_{9} (5))$

Step 6

Multiply $2$ by $2$ .

$4 \log_{9} (2) + 2 (- \log_{9} (5))$

Step 7

Multiply $- 1$ by $2$ .

$4 \log_{9} (2) - 2 \log_{9} (5)$