Precalculus Examples

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

Step 1

Simplify each term.

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Step 1.1

Logarithm base $2$ of $2$ is $1$ .

$2 \cdot 1 + 2 \log_{2} (6) - \log_{2} (3 \cdot 2)$

Step 1.2

Multiply $2$ by $1$ .

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

Step 1.3

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

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

Step 1.4

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

$2 + \log_{2} (36) - \log_{2} (3 \cdot 2)$

Step 1.5

Multiply $3$ by $2$ .

$2 + \log_{2} (36) - \log_{2} (6)$

Step 2

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

$2 + \log_{2} (\frac{36}{6})$

Step 3

Divide $36$ by $6$ .

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$4.58496250 \dots$