To determine which expression is equivalent to [tex]\(\log (6 \cdot 7)\)[/tex], we will use the properties of logarithms.
One of the key properties of logarithms is the product rule, which states:
[tex]\[
\log_b (a \cdot c) = \log_b (a) + \log_b (c)
\][/tex]
Here, we need to apply this rule to the logarithm with the given expression [tex]\(\log (6 \cdot 7)\)[/tex]. Let's break this down step by step:
1. Given expression: [tex]\(\log (6 \cdot 7)\)[/tex]
2. Apply the product rule of logarithms:
[tex]\[
\log (6 \cdot 7) = \log (6) + \log (7)
\][/tex]
Thus, by applying the product rule of logarithms, we find that [tex]\(\log (6 \cdot 7)\)[/tex] is equivalent to [tex]\(\log (6) + \log (7)\)[/tex].
Let's now review the given options and identify which one matches our derived expression:
A. [tex]\(\log (6) + \log (7)\)[/tex]
B. [tex]\(\log (6) \cdot \log (7)\)[/tex]
C. [tex]\(6 \cdot \log (7)\)[/tex]
D. [tex]\(\log (6) - \log (7)\)[/tex]
As we can see, option A is:
[tex]\[
\log (6) + \log (7)
\][/tex]
This matches our derived expression.
Therefore, the correct answer is:
[tex]\[
\boxed{\text{A}}
\][/tex]
