To solve the expression [tex]\(\log_6 60 - \log_6 30\)[/tex], we can use the properties of logarithms. Specifically, the property that states:
[tex]\[
\log_b(a) - \log_b(c) = \log_b\left(\frac{a}{c}\right)
\][/tex]
Applying this property:
[tex]\[
\log_6 60 - \log_6 30 = \log_6\left(\frac{60}{30}\right)
\][/tex]
Now, simplify the fraction within the logarithm:
[tex]\[
\frac{60}{30} = 2
\][/tex]
Therefore, our expression now becomes:
[tex]\[
\log_6 \left(2\right)
\][/tex]
This means the simplified form of [tex]\(\log_6 60 - \log_6 30\)[/tex] is:
[tex]\[
\log_6 2
\][/tex]
So, the correct answer is:
A. [tex]\(\log_6 2\)[/tex]
