To express [tex]\(\log_b \frac{G}{6}\)[/tex] as a difference of logarithms, we will utilize the properties of logarithms.
The logarithm property that we will use is:
[tex]\[
\log_b \left(\frac{M}{N}\right) = \log_b M - \log_b N
\][/tex]
This property states that the logarithm of a quotient is equal to the logarithm of the numerator minus the logarithm of the denominator.
Given the expression [tex]\(\log_b \frac{G}{6}\)[/tex]:
1. Identify the numerator and the denominator in the expression. Here, [tex]\(G\)[/tex] is the numerator and [tex]\(6\)[/tex] is the denominator.
2. Apply the logarithm quotient property.
So, we have:
[tex]\[
\log_b \frac{G}{6} = \log_b G - \log_b 6
\][/tex]
Therefore:
[tex]\[
\log_b \frac{G}{6} = \log_b G - \log_b 6
\][/tex]
Thus, the logarithm [tex]\(\log_b \frac{G}{6}\)[/tex] can be expressed as the difference of [tex]\(\log_b G\)[/tex] and [tex]\(\log_b 6\)[/tex], i.e., [tex]\(\log_b G - \log_b 6\)[/tex].
