Precalculus Examples

$\log_{4} (12)$

Step 1

Rewrite $\log_{4} (12)$ as $\log_{4} (2^{2} \cdot 3)$ .

$\log_{4} (2^{2} \cdot 3)$

Step 2

Rewrite $\log_{4} (2^{2} \cdot 3)$ as $\log_{4} (2^{2}) + \log_{4} (3)$ .

$\log_{4} (2^{2}) + \log_{4} (3)$

Step 3

Simplify each term.

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Step 3.1

Expand $\log_{4} (2^{2})$ by moving $2$ outside the logarithm.

$2 \log_{4} (2) + \log_{4} (3)$

Step 3.2

Logarithm base $4$ of $2$ is $\frac{1}{2}$ .

$2 (\frac{1}{2}) + \log_{4} (3)$

Step 3.3

Cancel the common factor of $2$ .

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Step 3.3.1

Cancel the common factor.

$2 (\frac{1}{2}) + \log_{4} (3)$

Step 3.3.2

Rewrite the expression.

$1 + \log_{4} (3)$