To simplify the expression [tex]\(\log 6 - \log 3 - \log 2\)[/tex], let's use the properties of logarithms. Specifically, we will use the property that states:
[tex]\[
\log a - \log b = \log \left(\frac{a}{b}\right)
\][/tex]
Following this property, let's work through the expression step by step:
1. Start with the expression:
[tex]\[
\log 6 - \log 3 - \log 2
\][/tex]
2. Apply the logarithm subtraction property to the first two terms:
[tex]\[
\log 6 - \log 3 = \log \left(\frac{6}{3}\right)
\][/tex]
Simplifying inside the log gives:
[tex]\[
\log \left(\frac{6}{3}\right) = \log 2
\][/tex]
3. Now we have:
[tex]\[
\log 2 - \log 2
\][/tex]
4. Again apply the logarithm subtraction property:
[tex]\[
\log 2 - \log 2 = \log \left(\frac{2}{2}\right)
\][/tex]
Simplifying inside the log gives:
[tex]\[
\log \left(\frac{2}{2}\right) = \log 1
\][/tex]
Since [tex]\(\log 1 = 0\)[/tex], we conclude:
[tex]\[
\log 6 - \log 3 - \log 2 = \log 1
\][/tex]
Thus, the correct answer is:
B. [tex]\(\log 1\)[/tex]
