Precalculus Examples

$2 \log_{7} (x + 4) + 7 \log_{7} (x + 6) - \frac{1}{2} \cdot \log_{7} (x)$

Step 1

Combine $\log_{7} (x)$ and $\frac{1}{2}$ .

$2 \log_{7} (x + 4) + 7 \log_{7} (x + 6) - \frac{\log_{7} (x)}{2}$

Step 2

To write $2 \log_{7} (x + 4)$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$7 \log_{7} (x + 6) + 2 \log_{7} (x + 4) \cdot \frac{2}{2} - \frac{\log_{7} (x)}{2}$

Step 3

Combine $2 \log_{7} (x + 4)$ and $\frac{2}{2}$ .

$7 \log_{7} (x + 6) + \frac{2 \log_{7} (x + 4) \cdot 2}{2} - \frac{\log_{7} (x)}{2}$

Step 4

Combine the numerators over the common denominator.

$7 \log_{7} (x + 6) + \frac{2 \log_{7} (x + 4) \cdot 2 - \log_{7} (x)}{2}$

Step 5

Multiply $2$ by $2$ .

$7 \log_{7} (x + 6) + \frac{4 \log_{7} (x + 4) - \log_{7} (x)}{2}$

Step 6

To write $7 \log_{7} (x + 6)$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$7 \log_{7} (x + 6) \cdot \frac{2}{2} + \frac{4 \log_{7} (x + 4) - \log_{7} (x)}{2}$

Step 7

Combine $7 \log_{7} (x + 6)$ and $\frac{2}{2}$ .

$\frac{7 \log_{7} (x + 6) \cdot 2}{2} + \frac{4 \log_{7} (x + 4) - \log_{7} (x)}{2}$

Step 8

Combine the numerators over the common denominator.

$\frac{7 \log_{7} (x + 6) \cdot 2 + 4 \log_{7} (x + 4) - \log_{7} (x)}{2}$

Step 9

Multiply $2$ by $7$ .

$\frac{14 \log_{7} (x + 6) + 4 \log_{7} (x + 4) - \log_{7} (x)}{2}$