Simplify/Condense log of 7- log of 3+ log of 6

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

Step 1

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

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

Step 2

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

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

Step 3

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\log (7 \cdot 2)$

Step 4

Multiply $7$ by $2$ .

$\log (14)$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\log (14)$

Decimal Form:

$1.14612803 \dots$