CAT 2017 Question Paper | Quants Slot 1

Logarithms is the most commonly tested topic in CAT. The basic concept is easy, learn the concepts and practice a wide range of CAT Questions from 2IIM. One can usually expect 2-3 questions from Logarithms and Exponents in the CAT exam. With every extra hour you log in for this topic, it becomes exponentially simpler. Here's one such question from Logarithm that has a layer of geometric on it.

Question 21 : Suppose, log₃x = log₁₂y = a, where x, y are positive numbers. If G is the geometric mean of x and y, and log₆G is equal to :

1. √a
2. 2a
3. \\frac{a}{2})
4. a

Video Explanation

Explanatory Answer

Method of solving this CAT Question from Exponents and Logarithms

log₃ x = log₁₂ y = a, where x, y are positive numbers.
log₃ x = a; x = 3^a
log₁₂ y = a; y = 12^a
If G is the geometric mean of x and y, log6G is equal to has to be found
We know that geometric mean is √xy
√xy = √(36^a)
= √(6^2a) = (6^2a)^{\\frac{1}{2})}
= 6^a
log₆ G = a

The question is "Suppose, log₃x = log₁₂y = a, where x, y are positive numbers. If G is the geometric mean of x and y, and log₆G is equal to :"

Hence, the answer is a