Precalculus Examples

$\log (\frac{t}{12})$

Step 1

Rewrite $\log (\frac{t}{12})$ as $\log (t) - \log (12)$ .

$\log (t) - \log (12)$

Step 2

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

$\log (t) - \log (2^{2} \cdot 3)$

Step 3

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

$\log (t) - (\log (2^{2}) + \log (3))$

Step 4

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

$\log (t) - (2 \log (2) + \log (3))$

Step 5

Apply the distributive property.

$\log (t) - (2 \log (2)) - \log (3)$

Step 6

Multiply $2$ by $- 1$ .

$\log (t) - 2 \log (2) - \log (3)$