Question

find out the expression I have given is POSITIVE or negative ????
HELP ME###

Answer 1

K^(1-x) = e^{e(1-x)} = e^{e - ex}
Log_e  K  = Log_e  e^e   = e * Log_e e   = e

Find when  K^(1-x) >  Log_e  K
      e^{e- ex}  >  e
      e^{e - e x }  / e  > 1
      e^{e - e x - 1} > 1
      e - ex - 1 >  0
      e x < e - 1
       x < (e -1)/e

So for      0 < x  <  (e-1)/e  , the given expression is positive.
                (e-1)/e < x < 1 ,  the expression is negative.