Precalculus Examples

$2 \log_{4} (16) + 2 \log_{4} (x) - \frac{1}{3} \log_{4} (x - 1)$

Step 1

Logarithm base $4$ of $16$ is $2$ .

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

Step 2

Simplify each term.

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Step 2.1

Multiply $2$ by $2$ .

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

Step 2.2

Combine $\log_{4} (x - 1)$ and $\frac{1}{3}$ .

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

Step 3

To write $4$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 4

Combine $4$ and $\frac{3}{3}$ .

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

Step 5

Combine the numerators over the common denominator.

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

Step 6

Multiply $4$ by $3$ .

$2 \log_{4} (x) + \frac{12 - \log_{4} (x - 1)}{3}$