Precalculus Examples

$\log_{2} (12) - 2 \log_{2} (6) + \log_{2} (2)$

Step 1

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

$\log_{2} (12 \cdot 2) - 2 \log_{2} (6)$

Step 2

Simplify each term.

Tap for more steps...

Step 2.1

Multiply $12$ by $2$ .

$\log_{2} (24) - 2 \log_{2} (6)$

Step 2.2

Simplify $- 2 \log_{2} (6)$ by moving $2$ inside the logarithm.

$\log_{2} (24) - \log_{2} (6^{2})$

Step 2.3

Raise $6$ to the power of $2$ .

$\log_{2} (24) - \log_{2} (36)$

Step 3

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\log_{2} (\frac{24}{36})$

Step 4

Cancel the common factor of $24$ and $36$ .

Tap for more steps...

Step 4.1

Factor $12$ out of $24$ .

$\log_{2} (\frac{12 (2)}{36})$

Step 4.2

Cancel the common factors.

Tap for more steps...

Step 4.2.1

Factor $12$ out of $36$ .

$\log_{2} (\frac{12 \cdot 2}{12 \cdot 3})$

Step 4.2.2

Cancel the common factor.

$\log_{2} (\frac{12 \cdot 2}{12 \cdot 3})$

Step 4.2.3

Rewrite the expression.

$\log_{2} (\frac{2}{3})$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\log_{2} (\frac{2}{3})$

Decimal Form:

$- 0.58496250 \dots$