CA Foundation · Quantitative Aptitude · Ratio and Proportion, Indices and Logarithms
If log (a/b) + log (b/c) + log (c/a) is evaluated, and separately if x = log₂ 3 · log₃ 4 · log₄ 5 · log₅ 6 · log₆ 7 · log₇ 8, then the value of x plus the first expression is:
The value is 3. The sum of the three logarithms equals log 1, which is zero. The chain product of logarithms telescopes to log base 2 of 8, which is 3. Adding them gives 3.
- A3Correct
- B0
- C1
- D6
Explanation
The first expression is log[(a/b)(b/c)(c/a)] = log 1 = 0. The product x telescopes by change of base to log₂ 8 = 3. Sum = 3 + 0 = 3.
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