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Question: Answered & Verified by Expert
If the reciprocals of 2, log3x-44 and log3x+724 are in arithmetic progression, then x is equal to
MathematicsSequences and SeriesJEE Main
Options:
  • A 1
  • B 2
  • C 4
  • D 0
Solution:
1906 Upvotes Verified Answer
The correct answer is: 2
Reciprocals of 2,log4log3x-4,log4log3x+72 are in A.P.
12,log3x-4log4,log3x+72log4 are in A.P.
12log4,log3x-4,log3x+72 are in A.P.
log2,log3x-4,log3x+72 are in A.P.
2,3x-4,3x+72 are in G.P.
3x-42=23x+72
Let 3x=y
y-42=2y+72
y2+16-8y=2y+7
y2-10y+9=0
y-1y-9=0y=1,9
3x=1,9x=0,2
But, for x=0,3x-4=-3<0
So, x=2 will only form an A.P.

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