CAT 2024 Slot 3 QA Q16 Logarithms & Exponents

Question 16 of the Quantitative Ability (QA) section, CAT 2024 Slot 3, with CAT's official answer and a worked solution.

If \(3^a=4,4^b=5,5^c=6,6^d=7,7^e=8\) and \(8^f=9\), then the value of the product abcdef is

TITA: type in the answer. There are no options and no negative marking.

Answer: 2 Logarithms & Exponents TITA

Solution

  1. \(a = \log_3 4, b = \log_4 5, \ldots, f = \log_8 9\).
  2. Chain rule of logs: product \(= \log_3 9 = 2\).

Same concept in other years

See every question on Chained logs telescope via change of base.

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