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If 1, log 3 3 1 - x + 2 , log 3 4.3 x - 1 are in arithmetic progression, then x equals

Options

  1. Alog 3 4
  2. B  1 - log 3 4
  3. C1 - log 4 3
  4. Dlog 4 3

Correct answer

B.   1 - log 3 4

Step-by-step solution

Since the given numbers are in AP, we get, 2 log 3 ( 3 1   -   x + 2 ) 1 / 2   = 1 + log 3 ( 4 . 3 x - 1 ) ⇒ log 3 3 1 - x + 2 = log 3 3 + log 3 4.3 x - 1 ⇒   3 1 - x + 2 = 3 ( 4 . 3 x - 1 ) ⇒   3 . 3 - x +   2 = 12 . 3 x - 3 Let, 3 x = t ∴ 3 t + 2 = 1 2 t - 3 ⇒   12 t 2 - 5 t - 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

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