Trigonometry Examples

$\log (3) + 2 \log (x) - \log (12)$

Step 1

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

$2 \log (x) + \log (\frac{3}{12})$

Step 2

Simplify each term.

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Step 2.1

Simplify $2 \log (x)$ by moving $2$ inside the logarithm.

$\log (x^{2}) + \log (\frac{3}{12})$

Step 2.2

Cancel the common factor of $3$ and $12$ .

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Step 2.2.1

Factor $3$ out of $3$ .

$\log (x^{2}) + \log (\frac{3 (1)}{12})$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $3$ out of $12$ .

$\log (x^{2}) + \log (\frac{3 \cdot 1}{3 \cdot 4})$

Step 2.2.2.2

Cancel the common factor.

$\log (x^{2}) + \log (\frac{3 \cdot 1}{3 \cdot 4})$

Step 2.2.2.3

Rewrite the expression.

$\log (x^{2}) + \log (\frac{1}{4})$

Step 3

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

$\log (x^{2} \frac{1}{4})$

Step 4

Combine $x^{2}$ and $\frac{1}{4}$ .

$\log (\frac{x^{2}}{4})$