CAT 2018 Question Paper | Quants Slot 1

CAT Questions

This wonderful question is based on Logarithms and Exponents. Historically, there has been at least one or two questions based on this topic. Solve this question to boost your confidence to crack the CAT exam. To practice more questions from CAT Previous Year Paper to ace your CAT online preparation, visit 2IIM's CAT Question Bank.

Question 11 : If x is a positive quantity such that 2^x = 3^log₅2 , then x is equal to

1. log₅9
2. 1 + log₅\\frac{3}{5})
3. 1 + log₃ (\\frac{5}{3}))
4. log₅8

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Video Explanation

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Explanatory Answer

Method of solving this CAT Question from Logarithms

Given, 2^x = 3^log₅2
Taking log on both sides, we get
log (2^x) = log (3^log₅2)
x × log(2) = log₅(2) × log(3)
x = \\frac{log_5 2 × log 3}{log 2})
Let us consider the base as 3,
x = \\frac{log_52 × log_3 3}{log_3 2})
x = \\frac{log_5 2 × 1}{log_3 2})
x = \\frac{1}{𝑙𝑜𝑔_2 5}) / \\frac{1}{𝑙𝑜𝑔_2 3}) = \\frac{log⁡_2 3}{𝑙𝑜𝑔_2 5}) = log₅(3)
Going through the options, Simplifying (B)
1 + log₅ (\\frac{3}{5}))
1 + log₅(3) - log₅(5)
1 + log₅(3) – 1
log₅(3)

The question is " If x is a positive quantity such that 2^x = 3^log₅2 , then x is equal to "

Hence, the answer is 1 + log₅\\frac{3}{5}).

Choice B is the correct answer.