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Question

The sum of the roots of the equation, x+12log2(3+2x)+2log4(102x)=0, is

A
log214
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B
log213
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C
log211
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D
log212
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Solution

The correct option is C log211
x+12log2(3+2x)+2log4(102x)=0
x+12log2(3+2x)+2log2(102x)log24=0
x+1+log2(102x)log2(3+2x)2=0
x+1log2((3+2x)2102x)=0
2x+1=9+62x+22x102x
202x2=9+62x+22x
(2x)214(2x)+11=0
Let two roots be 2x1 and 2x2
Then product of the roots:
2x12x2=112x1+x2=11x1+x2=log211
Sum of roots =log211

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