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If `log_(2)(5.2^(x)+1),log_(4)(2^(1-x)+1)` and 1 are in A.P,then x equalsA. `log^(5)`B. `1-log^(5)`C. `log_(5) 2`D. None of these |
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Answer» Correct Answer - 2 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.` |
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