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Question

The solution set of the equation xlogx(1x)2=9 is


A

{- 2, 4}

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B

{4}

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C

{0, - 2, 4}

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D

None of these

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Solution

The correct option is B

{4}


xlogx(1x)2=9

logx(9)=logx(1x)2(;∵ ax=NlogaN=x)

9=(1x2)1+x22x9=0

x22x8=0 ⇒ (x + 2)(x - 4) = 0 ⇒ x = -2, 4
But x>0; x=4


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