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

Question 1148535: If a and b are positive numbers such that a^b=b^a and b=9a, then what is the value of a?
Answer by ikleyn(52787) (Show Source): You can put this solution on YOUR website!
.


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

Solved and completed.

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