Precalculus Examples

$\log (3) - \log (12) + \log (6)$

Step 1

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

$\log (\frac{3}{12}) + \log (6)$

Step 2

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

$\log (\frac{3}{12} \cdot 6)$

Step 3

Cancel the common factor of $6$ .

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Step 3.1

Factor $6$ out of $12$ .

$\log (\frac{3}{6 (2)} \cdot 6)$

Step 3.2

Cancel the common factor.

$\log (\frac{3}{6 \cdot 2} \cdot 6)$

Step 3.3

Rewrite the expression.

$\log (\frac{3}{2})$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\log (\frac{3}{2})$

Decimal Form:

$0.17609125 \dots$