Algebra Examples

$\log_{2} (4) + \log_{2} (2) - \log_{2} (8)$

Step 1

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

$\log_{2} (4 \cdot 2) - \log_{2} (8)$

Step 2

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

$\log_{2} (\frac{4 \cdot 2}{8})$

Step 3

Cancel the common factor of $4$ and $8$ .

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Step 3.1

Factor $4$ out of $4 \cdot 2$ .

$\log_{2} (\frac{4 (2)}{8})$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $4$ out of $8$ .

$\log_{2} (\frac{4 \cdot 2}{4 \cdot 2})$

Step 3.2.2

Cancel the common factor.

$\log_{2} (\frac{4 \cdot 2}{4 \cdot 2})$

Step 3.2.3

Rewrite the expression.

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

Step 4

Cancel the common factor of $2$ .

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Step 4.1

Cancel the common factor.

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

Step 4.2

Rewrite the expression.

$\log_{2} (1)$

Step 5

Logarithm base $2$ of $1$ is $0$ .

$0$