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Question

The set of all values of x satisfying xlogx(1x)2=9 is


A

a subset of R containing N

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B

a subset of R containing Z(set of all integers)

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C

is a finite set containing at least two elements

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D

a finite set

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Solution

The correct option is D

a finite set


Taking algorithm of both the sides with base 3, we have
logx(1x)2log3x=2log3(1x)2log3x log3x=2 log3(1x)2=2 (1x)2=9 (clearly x3) x=4,2. But x>0 x=4


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