JEE Main 2021MathematicsSequences and SeriesMediumNumerical

JEE Main 2021 — Sequences and Series Question with Solution

JEE Main 2021 (27 Jul Shift 1)

Question

If log32,log32x-5,log32x-72 are in an arithmetic progression, then the value of x is equal to _____.

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Show full solutionCorrect answer: 3
Correct answer
3

Step-by-step explanation

As log32,log32x-5,log32x-72 are in arithmetic progression, 2log32x-5=log32+log32x-72

⇒log32x-52=log322x-72

Let 2x=t

So, log3t-52=log32t-72

⇒t-52=2t-7

⇒t2-12t+32=0

⇒t-4t-8=0

⇒2x=4 or 2x=8

Here, x≠2, as log34-5 does not exist. 

So, x=3

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About this question

This is a previous-year question from JEE Main 2021, covering the Sequences and Series chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.