Precalculus Examples

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

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Simplify $2 \log_{2} (12)$ by moving $2$ inside the logarithm.

$\log_{2} (12^{2}) - \log_{2} (4) + \log_{2} (3)$

Step 1.2

Raise $12$ to the power of $2$ .

$\log_{2} (144) - \log_{2} (4) + \log_{2} (3)$

Step 1.3

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

$\log_{2} (144) - 1 \cdot 2 + \log_{2} (3)$

Step 1.4

Multiply $- 1$ by $2$ .

$\log_{2} (144) - 2 + \log_{2} (3)$

Step 2

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\log_{2} (144 \cdot 3) - 2$

Step 3

Multiply $144$ by $3$ .

$\log_{2} (432) - 2$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\log_{2} (432) - 2$

Decimal Form:

$6.75488750 \dots$