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

Question

If 1, log 3 3 1 - x + 2 , log 3 4.3 x - 1 are in arithmetic progression, then x equals, log 3 4, 1 - log 3 4, 1 - log 4 3, log 4 3

MARKS App · Accepted Answer

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

Search any question & find its solution

Looking for more such questions to practice?