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Question

If log2(5×2x+1),log4(21x+1) and 1 are in A.P., then x equals

A
log25
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B
1log52
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C
log52
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D
1log25
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Solution

The correct option is D 1log25
The given numbers are in A.P. so,
2log4(21x+1)=1+log2(5×2x+1)2log22(22x+1)=log22+log2(5×2x+1)22log2(22x+1)=log22(5×2x+1)(22x+1)=2(5×2x+1)
Assuming 2x=y
2y+1=10y+210y2+y2=0(5y2)(2y+1)=0y=25 or 122x=25 or 122x=25[2xcannot be negative]
x=log2(2/5)=1log25

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