Write as a Single Logarithm ( log of 3- log of 6)+ log of 2

$(\log (3) - \log (6)) + \log (2)$

Step 1

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

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

Step 2

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

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

Step 3

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

Divide $3$ by $3$ .

$\log (1)$

Step 5

Logarithm base $10$ of $1$ is $0$ .

$0$