CAT 2020 Slot 1 QA Q5 Logarithms & Exponents

Question 5 of the Quantitative Ability (QA) section, CAT 2020 Slot 1, with CAT's official answer and a worked solution.

If log4 5 = (log4 y) (log6 √5), then y equals

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

Answer: 36 Logarithms & Exponents TITA

Solution

  1. Write in natural logs: \(\frac{\ln5}{\ln4} = \frac{\ln y}{\ln4}\cdot\frac{\frac12\ln5}{\ln6}\).
  2. Cancel \(\frac{\ln5}{\ln4}\): \(1 = \frac{\ln y}{2\ln6}\), so \(\ln y = \ln36\) and \(y=36\).

Same concept in other years

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

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