To find the value of [tex]\(\log_8 24\)[/tex], we can use the change of base formula for logarithms. According to the change of base formula, [tex]\(\log_b a\)[/tex] can be calculated using common logarithms (base 10) or natural logarithms (base [tex]\(e\)[/tex]) as follows:
[tex]\[
\log_b a = \frac{\log a}{\log b}
\][/tex]
In this case, we want to find [tex]\(\log_8 24\)[/tex]. Applying the formula, we get:
[tex]\[
\log_8 24 = \frac{\log 24}{\log 8}
\][/tex]
Upon evaluating the logarithmic expressions in this fraction, we find that:
[tex]\[
\log_8 24 \approx 1.5283208335737188
\][/tex]
Thus, the approximate value of [tex]\(\log_8 24\)[/tex] is closest to the option B, which is 1.53. So, the correct answer is:
B. 1.53
