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Question

If 6(logx2−log4x)+7=0, then find the values of x

A
x=8 or x=223
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B
x=7 or x=223
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C
x=6 or x=223
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D
none of these
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Solution

The correct option is A x=8 or x=223
6(logx2log4x)+7=0
or 6(logx212log2x)+7=0
or 6(1yy2)+7=0 (where y=log2x)
or 6(2y22y)+7=0
or 3(2y2y)+7=0
or 63y2+7y=0
or 3y27y6=0
or y2+2y9y6=0
or (y3)(3y+2)=0
or y=3 or y=23
log2x=3 or 23
or x=8 or x=223

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