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Question

The set of real values of x satisfying the equation
|x1|log3(x2)2logx(9)=(x1)7
is


A

{2}

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B

{27, 81}

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C

{81}

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D

{2, 81}

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Solution

The correct option is C

{81}


|x1|log3(x2)2logx(9)=(x1)7(log3x22logx9)log|x1||x1|=7log|x1|(x1)log3x22logx9=72log3x4×1log3x=7Let log3x=t2t4t=72t27t4=0(t4)(2t+1)=0t=4,t=12log3x=4 log3x=12x=81,x=13<1 x13


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