CMA Foundation · Fundamentals of Business Mathematics and Statistics · Indices and Logarithms
Given log 2 = 0.3010 and log 3 = 0.4771 (common logarithms), what is the value of log 72?
Log 72 is about 1.857. Writing 72 as 2 cubed times 3 squared, the product and power laws give 3 times log 2 plus 2 times log 3, which is 0.9030 plus 0.9542, roughly 1.8572, matching the option 1.8573.
- A1.8573Correct
- B1.5563
- C1.8062
- D1.3802
Explanation
72 = 2^3 x 3^2. So log 72 = 3(0.3010) + 2(0.4771) = 0.9030 + 0.9542 = 1.8572. Check: 0.9030 + 0.9542 = 1.8572, so the nearest option is 1.8573 only if rounding; recomputing exactly gives 1.8572, which is closest to the key. The other options use wrong exponents such as 2^2 x 3^3.
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