# IPM Sample Paper 2020 | IPM Rohtak Quantitative Aptitude

###### IPMAT Sample Paper | IPMAT Question Paper | Question 40

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Question 40 : If log 2, log (2x - 1) and log (2x + 3) are in A.P, then x is equal to ____

1. $$frac{5}{2}\\$ 2. log25 3. log32 4. 32 ## 🚀 Introductory Offer! Buy CAT'21 95-99 Booster Course for just Rs. 4500 Valid until 19th Sep #### 2IIM : Best Online CAT Coaching. ## Best CAT Coaching in Chennai #### CAT Coaching in Chennai - CAT 2021Online Batches Available Now! ### Explanatory Answer log 2 , log$2x-1) , log (2x+3) are in A.P. implies that 2, (2x-1) and (2x+3) are in G.P.

When 3 three terms a, b, c are in G.P. b becomes the Geometric Mean of a, b

Therefore, (2x-1) is the Geometric Mean of 2 and (2x+3)

(2x-1)2 = 2 * (2x+3)
4x2 + 1 - 4x = 4x + 6
4x2 – 8x – 5 = 0
(2x - 5) (2x + 1) = 0

x = $$frac{5}{2}\\$ or x = -$\frac{1}{2}\\$ When x = -$\frac{1}{2}\\$, the second term becomes, log$-2). Since log(negative number) is not legal. x = $$frac{5}{2}\\$ Therefore, the value of x = $\frac{5}{2}\\$. The question is "If log 2, log$2x - 1) and log (2x + 3) are in A.P, then x is equal to ____"

##### Hence, the answer is $$frac{5}{2}\\$ Choice A is the correct answer ###### Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! ###### Already have an Account? ##### 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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