Math miscellaneousHard

Question

If 1, logg (31-x + 2), log3 (4.3x - 1) are in A.P. then x equals

Options

A.log3 4
B.1 + log3 4
C.1 - log3 4
D.log4 3

Solution

1, logg (31-x + 2), log3(4.3x - 1) are in A.P.
⇒ 2 logg (31-x + 2) = 1 + log3 (4.3x - 1)
log3(31-x + 2) = log3 3 + log4 (4.3x- 1)
log3(31-x + 2) = log3 [3(4.3x - 1)]
31-x + 2 = 3(4.3x - 1)(put 3x = t)
+ 2 = 12t - 3 or 12t2 - 5t - 3 = 0
Hence t = - ⇒ 3x = ⇒ x = log3 or x = log3 + - log3 4 ⇒ x = 1 - log34

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