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Question 11 : If x is a positive quantity such that 2x = 3log52 , 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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Explanatory Answer

Method of solving this CAT Question from Logarithms

Given, 2x = 3log52
Taking log on both sides, we get
log (2x) = log (3log52)
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

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

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

Choice B is the correct answer.


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