Precalculus Examples

$\log_{9} (60)$

Step 1

Rewrite $\log_{9} (60)$ as $\log_{9} (2^{2} \cdot 3 \cdot 5)$ .

$\log_{9} (2^{2} \cdot 3 \cdot 5)$

Step 2

Rewrite $\log_{9} (2^{2} \cdot 3 \cdot 5)$ as $\log_{9} (2^{2} \cdot 3) + \log_{9} (5)$ .

$\log_{9} (2^{2} \cdot 3) + \log_{9} (5)$

Step 3

Simplify each term.

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Step 3.1

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

$\log_{9} (2^{2}) + \log_{9} (3) + \log_{9} (5)$

Step 3.2

Simplify each term.

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Step 3.2.1

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

$2 \log_{9} (2) + \log_{9} (3) + \log_{9} (5)$

Step 3.2.2

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

$2 \log_{9} (2) + \frac{1}{2} + \log_{9} (5)$