If 1, log9(31–x + 2) and log3(4.3x –1) are in A.P. ,then x i... | MATH - ARITHMETIC PROGRESSION | SolveeIt | Solveeit

Today, August 19

Question

If 1, log₉(3^1–x + 2) and log₃(4.3^x –1) are in A.P. ,then x is equal to –

A

log₄3

B

log₃4

C

1 – log₃ 4

D

log₃ 0.25

Answer

1 – log₃ 4

Explanation

Solution

1, log₉(3^1–x + 2), log₃ (4.3^x – 1) A.P.

log₃3, log₃(3^{1– x}+2)^1/2, log₃(4.3^x–1) A. P.

(3^1–x + 2) = 3. (4.3^x –1) ̃ 3.3^–x + 2 = 12.3^x – 3, 3^x = t

3/t + 2 = 12t – 3 ̃ 12t – 3/t– 5 = 0 ̃ 12t² – 5t – 3 = 0

12t² – 9t + 4t – 3 = 0

̃ 3t(4t – 3) +1 (4t –3) = 0, t =–1/3,

t = 3/4 ̃3^x = –1/3, 3^x = 3/4

̃x = log₃3 – log₃4 = 1 – log₃4