SOLUTION: If a and b are positive numbers such that a^b=b^a and b=9a, then what is the value of a?

If   =   and  b = 9a,  then


     = ,


     = ;


        then, since indexes on the left and on the right are equal, the bases    and    must be equal too,  which gives

     = 9a.


It gives

     = 9.

which implies

    a =  = .    ANSWER