CMA Foundation · Fundamentals of Business Mathematics and Statistics · Indices and Logarithms
Given log 2 = 0.3010 and log 3 = 0.4771 (base 10), what is the value of log 72?
Log 72 is about 1.857. Writing 72 as 2 cubed times 3 squared, the power and product laws give 3 times 0.3010 plus 2 times 0.4771, which is 0.9030 plus 0.9542, equal to 1.8572, so the nearest listed value is 1.8573.
- A1.6532
- B1.8573Correct
- C1.9542
- D2.0792
Explanation
72 = 2^3 x 3^2. So log 72 = 3(0.3010) + 2(0.4771) = 0.9030 + 0.9542 = 1.8572, which rounds to 1.8573 in the options as given by the data (0.9030 + 0.9542 = 1.8572). Check: 1.8572 is the nearest listed value. The option 1.9542 comes from using 2 x log 2 + 3 x log 3 wrongly... actually it treats exponents swapped as 2(0.3010)+3(0.4771)=2.0333, so it is not valid.
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