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Question

If log2(4x+1+4)log2(4x+1)=log28, then x equals


A

-1

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B

0

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C

1

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D

2

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Solution

The correct option is B

0


log2(4x+1+4)log2(4x+1)=log28log24(4x+1) log2(4x+1)=3Let 4x+1=tlog24tlog2t=3(log24+log2t)log2t=3(2+log2t)log2t=3(log2t)2+2log2t3=0(log2t)2log2t+3log2t3=0log2t(log2t1)+3(log2t1)=0log2t=3 log2t=1log2(4x+1)=3 log2(4x+1)=14x+1=18 4x+1=24x78 4x=1 x=0


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