Precalculus Examples

$\log_{9} (36)$

Step 1

Rewrite $\log_{9} (36)$ as $\log_{9} (2^{2} \cdot 3^{2})$ .

$\log_{9} (2^{2} \cdot 3^{2})$

Step 2

Rewrite $\log_{9} (2^{2} \cdot 3^{2})$ as $\log_{9} (2^{2}) + \log_{9} (3^{2})$ .

$\log_{9} (2^{2}) + \log_{9} (3^{2})$

Step 3

Simplify each term.

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Step 3.1

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

$2 \log_{9} (2) + \log_{9} (3^{2})$

Step 3.2

Expand $\log_{9} (3^{2})$ by moving $2$ outside the logarithm.

$2 \log_{9} (2) + 2 \log_{9} (3)$

Step 3.3

Logarithm base $9$ of $3$ is $\frac{1}{2}$ .

$2 \log_{9} (2) + 2 (\frac{1}{2})$

Step 3.4

Cancel the common factor of $2$ .

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Step 3.4.1

Cancel the common factor.

$2 \log_{9} (2) + 2 (\frac{1}{2})$

Step 3.4.2

Rewrite the expression.

$2 \log_{9} (2) + 1$