CAT Quantitative Aptitude Questions | CAT Logarithms and Exponents

CAT Questions | Logarithms and Exponents | Logarithm - Identities

The question is from Log and Exponents. We can solve this easily using log identities. We need to find out the value of a log given an equation. With every extra hour you log in for this topic, it becomes exponentially simpler. CAT Logarithms and Exponents is a favorite in CAT Exam, and appears more often than expected in the CAT Quantitative Aptitude section in the CAT Exam

Question 8: logxy + logyx2 = 3. Find logxy3.

  1. 4
  2. 3
  3. 31/2
  4. 31/16

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Explanatory Answer

Method of solving this CAT Question from Logs and Exponents: Application of Basic Identities!!

logxy + logyx2 = 3
Let a = logxy
logx3 = \\frac{1}{log_3{x}}\\)
logyx2 = 2logyx
We know that logyx = \\frac{1}{log_x{y}}\\)
Hence form above logyx = \\frac{1}{a}\\)
Now rewritting the equation logxy + logyx2 = 3
Using a we get a + \\frac{2}{a}\\) = 3
i.e., a2 - 3a + 2 = 0
Solving we get a = 2 or 1
If a = 2, Then logxy = 2 and logyx3 = 3
logxy = 3 * 2 = 6
Or
If a = 1, Then logxy = 1 and logyx3 = 3
logxy = 3 * 1 = 3

The question is "Find logxy3."

Hence, the answer is "3".

Choice B is the correct answer.


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