Precalculus Examples

$\log_{2} (12) - 2 \log_{2} (6) + \log_{2} (24)$

Step 1

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

$\log_{2} (12 \cdot 24) - 2 \log_{2} (6)$

Step 2

Simplify each term.

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Step 2.1

Multiply $12$ by $24$ .

$\log_{2} (288) - 2 \log_{2} (6)$

Step 2.2

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

$\log_{2} (288) - \log_{2} (6^{2})$

Step 2.3

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

$\log_{2} (288) - \log_{2} (36)$

Step 3

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

$\log_{2} (\frac{288}{36})$

Step 4

Logarithm base $2$ of $\frac{288}{36}$ is $3$ .

$3$