Evaluate , to three decimal places.

Question

BlackTom AI · Accepted Answer

To start, I will restate the problem and the available choices to ensure we’re analyzing the right items.
Question: Evaluate log base 2 of 24, to three decimal places.
Answer options: 4.585, 0.218, 19.000, 3.974.

Now, assess each option one by one:
Option A: 4.585. This value corresponds to the actual decimal approximation of log2(24). Using the change-of-base formula log2(24) = ln(24)/ln(2) and evaluating with common natural logarithms gives ln(24) ≈ 3.178054 and ln(2) ≈ 0.693147. Dividing yields ≈ 4.585, which rounds to three decimals as 4.585. This option is consistent with the logarithm’s properties and the required precision.

Option B: 0.218. This is far smaller than the true value; it could arise from confusing log base 24 of 2 or some reciprocal form, but it does not match log2(24). If you mistakenly inverted the logarithm or used an incompatible base, you could land in the 0.2 range, but that would be incorrect for log base 2 of 24.

Option C: 19.000. This is orders of magnitude off from the correct result. A value near 19 would imply an extremely large ratio of 24 to the base 2, which doesn’t fit the actual logarithm. It suggests a miscalculation or misinterpretation of the logarithm operation.

Option D: 3.974. This is closer to the correct scale but still not accurate to three decimals. If one approximates using rough mental math, one might land in the 3.9–4.0 range, but 3.974 does not match the precise value obtained from ln-based computation, and would be considered incorrect for three-decimal accuracy.

In summary, the correct reasoning shows log2(24) ≈ 4.585 when rounded to three decimals, while the remaining options reflect common missteps or rounding errors rather than the true value.

MHF4U - Quattrociocchi - S1 Unit 6 Online Quiz

Evaluate , to three decimal places.

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