# CAT 2018 Question Paper | Quants Slot 1

###### CAT Previous Year Paper | CAT Logarithm Questions | Question 11

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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 ## 7,400/- off on 74th Independence Day! Kickstart your prep now! #### 2IIM : Best Online CAT Coaching. ### Video Explanation ## Best CAT Coaching in Chennai #### CAT Coaching in Chennai - CAT 2020Online Batches Available 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. ###### 7,400/- off on 74th Independence Day! Kickstart your prep now! Offer until 16th Aug. ###### Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2020Enroll at 30,000/- Online Classroom Batches Starting Now! ###### Best CAT Coaching in ChennaiPrices slashed by Rs 5000/- Attend a Demo Class ##### 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? Phone:$91) 44 4505 8484
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