To find an expression equivalent to [tex]\(\log \left(12^8\right)\)[/tex], we can use one of the logarithmic properties known as the power rule. The power rule states that:
[tex]\[
\log_b (a^c) = c \cdot \log_b (a)
\][/tex]
In this case, we have [tex]\(a = 12\)[/tex], [tex]\(c = 8\)[/tex], and we are assuming the base [tex]\(b\)[/tex] is 10 (common logarithm) unless specified otherwise. Applying the power rule, we get:
[tex]\[
\log (12^8) = 8 \cdot \log (12)
\][/tex]
So, by using the power rule, we see that [tex]\(\log (12^8)\)[/tex] is equivalent to [tex]\(8 \cdot \log (12)\)[/tex].
Therefore, the correct answer is:
A. [tex]\(8 \cdot \log (12)\)[/tex]
