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Question

The solution set of  2log2log2x+log1/2log2(22x)=1 is


  1. {2,4}
     

  2. {4,8}
     

  3. {1/2,4}
     

  4. {8}
     


Solution

The correct option is D

{8}
 


log22log2x+log1/2log2(22x)=1log2log2x2+log1/2log2(8x)12=1log2log2x2+log1/212+log1/2log28x=1log2log2x2=log1/2log28xlog2log2x2=log2log28xx2=8xx28x=0x(x8)=0x=8

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