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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_(2)5`B. `1-log_(2)5`C. `log_(5)2`D. none of these |
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Answer» Correct Answer - B The given number are in A.P. `:." "2log_(4)(2^(1-x)+1)=log_(2)(5.2^(x)+1)+1` `rArr" "2log_(2)2((2)/(2^(x))+1)=log_(2)(5.2^(x)+1)+log_(2)2` `rArr" "(2)/(2)log_(2)((2)/(2^(x))+1)=log_(2)(5.2^(x)+1)2` `rArr" "log_(2)((2)/(2^(x))+1)=log_(2)(10.2^(x)+2)` `rArr" "(2)/(2^(x))+1=10.2^(x)+2` `rArr" "(2)/(y)+1=10y+2," where"2^(x)=y` `:." "10y^(2)+y-2=0` `rArr" "(5y-2)(2y+1)=0` `rArr" "y=2//5" "[becausey=2^(x)gt0]` `rArr" "2^(x)=2//5rArrx=log_(2)(2//5)=log_(2)2-log_(2)5=1-log_(2)5` |
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