If `log_(2)(5.2^(x)+1),log_(4)(2^(1-x)+1)` and 1 are in A.P,then x equals

Options

A. `log^(5)`
B. `1-log^(5)`
C. `log_(5) 2`
D. None of these

Answer

2

Explanation

The given no are in A.P
`rArr 2 log_(4) (2^(1-x)+12)=log_(2)(5.2^(x)+1)+1`
`rarr 2 log_(2)((2)/(2^(x))+1) = log_(2) (5.2^(x)+1)+ log_(2)`
`rArr (2)/(2) log_(2) (2)/(2^(x))+1=10.2^(x)+2`
`rArr2/y+1=10y+2`
`rArr10 Y^(2)+y-2=0`
`rArr y=2/5 or y= -1/2`
`rArr 2^(x)=2//5 or 2^(x) =-1/2`
`rArr x=log_(2)(2//5)`
`rArr x=log_(2)- log_(2)5`
`rArr x= 1-log_(2)5.`