Trigonometry Examples

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

Step 1

Simplify each term.

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Step 1.1

Simplify $2 \log (3)$ by moving $2$ inside the logarithm.

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

Step 1.2

Raise $3$ to the power of $2$ .

$\log (9) + 2 \log (x) - \log (12)$

Step 1.3

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

$\log (9) + \log (x^{2}) - \log (12)$

Step 2

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

$\log (9 x^{2}) - \log (12)$

Step 3

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

$\log (\frac{9 x^{2}}{12})$

Step 4

Cancel the common factor of $9$ and $12$ .

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Step 4.1

Factor $3$ out of $9 x^{2}$ .

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $3$ out of $12$ .

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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