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Question

If x satisfies the equation log1/3(x1)+log1/3(x+1)+log3(5x)<1, then x lies in the interval

A
(1,3)
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B
(2,5)
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C
(1,2)
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D
(4,)
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Solution

The correct option is B (2,5)
log1/3(x1)+log1/3(x+1)+log3(5x) is valid when x1>0,x+1>0,5x>0
1<x<5 ...(1)
log1/3(x1)+log1/3(x+1)+log3(5x)<1
log3(x1)log3(x+1)+2log3(5x)<1[log1/ab=logab]
log3(5x)2(x1)(x+1)<1
(5x)2(x1)(x+1)<3
x210x+25<3x23
x2+5x14>0
x<7 and x>2 ...(2)
From (1) & (2), we get x(2,5)

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