Precalculus Examples

$\log_{b} (x) + \log_{b} (x + 3) - \log_{b} (12)$

Step 1

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

$\log_{b} (x) + \log_{b} (x + 3) - \log_{b} (2^{2} \cdot 3)$

Step 2

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

$\log_{b} (x) + \log_{b} (x + 3) - (\log_{b} (2^{2}) + \log_{b} (3))$

Step 3

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

$\log_{b} (x) + \log_{b} (x + 3) - (2 \log_{b} (2) + \log_{b} (3))$

Step 4

Apply the distributive property.

$\log_{b} (x) + \log_{b} (x + 3) - (2 \log_{b} (2)) - \log_{b} (3)$

Step 5

Multiply $2$ by $- 1$ .

$\log_{b} (x) + \log_{b} (x + 3) - 2 \log_{b} (2) - \log_{b} (3)$