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Question

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


A

{8}

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B

{2,4}

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C

{4,8}

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D

{1/2,4}

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Solution

The correct option is A

{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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