Precalculus Examples

$\log (7) + \log (6) - \log (3)$

Step 1

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

$\log (7 \cdot 6) - \log (3)$

Step 2

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

$\log (\frac{7 \cdot 6}{3})$

Step 3

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

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Step 3.1

Factor $3$ out of $7 \cdot 6$ .

$\log (\frac{3 (7 \cdot 2)}{3})$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $3$ out of $3$ .

$\log (\frac{3 (7 \cdot 2)}{3 (1)})$

Step 3.2.2

Cancel the common factor.

$\log (\frac{3 (7 \cdot 2)}{3 \cdot 1})$

Step 3.2.3

Rewrite the expression.

$\log (\frac{7 \cdot 2}{1})$

Step 3.2.4

Divide $7 \cdot 2$ by $1$ .

$\log (7 \cdot 2)$

Step 4

Multiply $7$ by $2$ .

$\log (14)$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\log (14)$

Decimal Form:

$1.14612803 \dots$