Precalculus Examples

$\log_{2} (48) + \log_{2} (6) - \log_{2} (9)$

Step 1

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

$\log_{2} (48 \cdot 6) - \log_{2} (9)$

Step 2

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

$\log_{2} (\frac{48 \cdot 6}{9})$

Step 3

Cancel the common factor of $48$ and $9$ .

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Step 3.1

Factor $3$ out of $48 \cdot 6$ .

$\log_{2} (\frac{3 (16 \cdot 6)}{9})$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $3$ out of $9$ .

$\log_{2} (\frac{3 (16 \cdot 6)}{3 (3)})$

Step 3.2.2

Cancel the common factor.

$\log_{2} (\frac{3 (16 \cdot 6)}{3 \cdot 3})$

Step 3.2.3

Rewrite the expression.

$\log_{2} (\frac{16 \cdot 6}{3})$

Step 4

Cancel the common factor of $6$ and $3$ .

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Step 4.1

Factor $3$ out of $16 \cdot 6$ .

$\log_{2} (\frac{3 (16 \cdot 2)}{3})$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $3$ out of $3$ .

$\log_{2} (\frac{3 (16 \cdot 2)}{3 (1)})$

Step 4.2.2

Cancel the common factor.

$\log_{2} (\frac{3 (16 \cdot 2)}{3 \cdot 1})$

Step 4.2.3

Rewrite the expression.

$\log_{2} (\frac{16 \cdot 2}{1})$

Step 4.2.4

Divide $16 \cdot 2$ by $1$ .

$\log_{2} (16 \cdot 2)$

Step 5

Simplify the expression.

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Step 5.1

Multiply $16$ by $2$ .

$\log_{2} (32)$

Step 5.2

Logarithm base $2$ of $32$ is $5$ .

$5$