Q29 / 118 · NTA Abhyas (JEE Main) 2020 · Mathematics · Sequences and Series

If 1, log331-x+2, log34.3x-1 are in arithmetic progression, then x equals

  • A
    log34
  • Correct answer
    B
     1-log34
  • C
    1-log43
  • D
    log43

Solution

Since the given numbers are in AP, we get,
   2log3(31 - x+2)1/2 =1+log3(4.3x-1)

⇒ log 3 3 1 - x + 2 = log 3 3 + log 3 4.3 x - 1

⇒ 31-x+2=3(4.3x-1)

⇒ 3.3-x+ 2=12.3x-3

Let, 3x=t

∴ 3 t + 2 = 1 2 t - 3

⇒ 12t2-5t-3=0

⇒ t = - 1 3 , 3 4

∴ 3 x = 3 4 ∵ 3 x  cannot be negative

⇒ x = log 3 3 4 ⇒ x = 1 - log 3 4

Hence, the correct answer is option: 'B'.

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