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iit jee Grade: 12
        

SOLVE


log(x+4)/2{log2(2x-1)/(3+x)}<0

7 years ago

Answers : (1)

Badiuddin askIITians.ismu Expert
147 Points
										

Dear


 


case 1    (x+4)/2 >1


   x> -2


log(x+4)/2{log2(2x-1)/(3+x)}<0


so   0  <  log2(2x-1)/(3+x) <1


       1  <  (2x-1)/(3+x) <  2  


  1  <  (2x-1)/(3+x)                           and         (2x-1)/(3+x) <2


  x>4                                                    and         for all x


 so solution is x>4


 


case 2    0<(x+4)/2 <1


                  -4 <x<-2


    


log(x+4)/2{log2(2x-1)/(3+x)}<0


so    log2(2x-1)/(3+x) >1


        (2x-1)/(3+x) >  2  


 now again let  x+3 > 0


  2x-1 > 6+2x


    no solution


   x+3 <0


   x<-3


 so   2x-1 < 6+2x


   all x


 so final solution is    -4<x<-3


 


so solution for x is     -4<x<-3   and x>4


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Badiuddin


 


 


 


  


 


                             

7 years ago
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