The Domain of f(x) =log1 /2.log4.log3[(x-lambda)2] (where [ ] denotes the greatest integer function) is (-infinity,2] U [6,infinity) , then thevalue of lambda is:-

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We havefx=log12log4log3x-λ2Quantity inside log must be positive, hencex-λ2>0x-,-λ....ilog3x-λ2>0x-λ2>1x-λ2-1>0x-λ-1x-λ+1>0x-λ+1x-λ-1>0x-,λ-1λ+1,....iilog4log3x-λ2>0log4x-λ2>1x-λ2>4x-λ2-22>0x-λ-2x-λ+2>0x-λ+2x-λ-2>0x-,λ-2λ+2,....iiiTaking intersection of i,ii,iii getx-,λ-2λ+2, when λ=4x-,4-24+2,x-,26,Hence option4 is correct.

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