Precalculus Examples

$\log_{6} (\frac{b}{12})$

Step 1

Rewrite $\log_{6} (\frac{b}{12})$ as $\log_{6} (b) - \log_{6} (12)$ .

$\log_{6} (b) - \log_{6} (12)$

Step 2

Rewrite $\log_{6} (12)$ as $\log_{6} (2^{2} \cdot 3)$ .

$\log_{6} (b) - \log_{6} (2^{2} \cdot 3)$

Step 3

Rewrite $\log_{6} (2^{2} \cdot 3)$ as $\log_{6} (2^{2}) + \log_{6} (3)$ .

$\log_{6} (b) - (\log_{6} (2^{2}) + \log_{6} (3))$

Step 4

Expand $\log_{6} (2^{2})$ by moving $2$ outside the logarithm.

$\log_{6} (b) - (2 \log_{6} (2) + \log_{6} (3))$

Step 5

Apply the distributive property.

$\log_{6} (b) - (2 \log_{6} (2)) - \log_{6} (3)$

Step 6

Multiply $2$ by $- 1$ .

$\log_{6} (b) - 2 \log_{6} (2) - \log_{6} (3)$