# 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 ## Best CAT Online Coaching Try upto 40 hours for free Learn from the best! #### 2IIM : Best Online CAT Coaching. ### Video Explanation ## Best CAT Coaching in Chennai #### CAT Coaching in Chennai - CAT 2022Limited 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. ###### Prepare for CAT 2023 with 2IIM's Daily Preparation Schedule ###### Know all about CAT Exam Syllabus and what to expect in CAT ###### Best CAT Online Coaching Try upto 40 hours for free Learn from the best! ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2023 Classroom Batches Starting Now! @Gopalapuram ###### Best CAT Coaching in Chennai Introductory offer of 5000/- Attend a Demo Class ###### Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! ##### 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
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