To solve the logarithmic expression [tex]\(\log_8 8\)[/tex], we'll break it down step-by-step.
The logarithmic expression [tex]\(\log_b a\)[/tex] asks the question: "To what power must the base [tex]\(b\)[/tex] be raised to obtain the number [tex]\(a\)[/tex]?"
In this specific case, the expression is [tex]\(\log_8 8\)[/tex]. Here, our base [tex]\(b\)[/tex] is 8, and the number [tex]\(a\)[/tex] is also 8.
So, we're trying to find the exponent [tex]\(x\)[/tex] such that:
[tex]\[ 8^x = 8 \][/tex]
Since [tex]\(8^1 = 8\)[/tex], it is clear that:
[tex]\[ x = 1 \][/tex]
Therefore, the value of [tex]\(\log_8 8\)[/tex] is:
[tex]\[ \log_8 8 = 1 \][/tex]
So, [tex]\(\boxed{1}\)[/tex] is the answer.
