Answered

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What is the approximate value of this logarithmic expression? [tex]\(\log_8 24\)[/tex]

A. 0.90
B. 1.53
C. 0.48
D. 1.38

Sagot :

GinnyAnswer
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
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