Precalculus Examples

$\log_{9} (100)$

Step 1

Rewrite $\log_{9} (100)$ as $\log_{9} (2^{2} \cdot 5^{2})$ .

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

Step 2

Rewrite $\log_{9} (2^{2} \cdot 5^{2})$ as $\log_{9} (2^{2}) + \log_{9} (5^{2})$ .

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

Step 3

Simplify each term.

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Step 3.1

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

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

Step 3.2

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

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