If log2(5×2x+1),log4(21−x+1) and 1 are in A.P., then x equals
A
log25
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B
1−log52
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C
log52
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D
1−log25
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Solution
The correct option is D1−log25 The given numbers are in A.P. so, 2log4(21−x+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+2⇒10y2+y−2=0⇒(5y−2)(2y+1)=0⇒y=25 or −12⇒2x=25 or −12⇒2x=25[∵2xcannot be negative] ⇒x=log2(2/5)=1−log25