🎉 Ace XAT 2025 with 2IIM's Crash Course - Enrol now


🎉Effortlessly calculate your score with the 2IIM Score Calculator!🎉

CAT 2018 Question Paper | Quants Slot 1

CAT Previous Year Paper | CAT Logarithm Questions | Question 11

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 2x = 3log52 , then x is equal to

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

🎉 Ace XAT 2025 with 2IIM's Crash Course - Enrol now


Best CAT Online Coaching
Try upto 40 hours for free
Learn from the best!


2IIM : Best Online CAT Coaching.

🎉Effortlessly calculate your score with the 2IIM Score Calculator!🎉


2IIM : Best Online CAT Coaching.


Video Explanation


Best CAT Coaching in Chennai


CAT Coaching in Chennai - CAT 2022
Limited Seats Available - Register Now!


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
log5(3)

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.

 

CAT Questions | CAT Quantitative Aptitude

CAT Questions | Verbal Ability for CAT


Where is 2IIM located?

2IIM Online CAT Coaching
A Fermat Education Initiative,
58/16, Indira Gandhi Street,
Kaveri Rangan Nagar, Saligramam, Chennai 600 093

How to reach 2IIM?

Mobile: (91) 99626 48484 / 94459 38484
WhatsApp: WhatsApp Now
Email: info@2iim.com