There are infinitely many solutions, here's one, approximately:



a=0.5, x=0.03125, y=0.642286







, approximately



----------------------------



here's another, approximately:



a=1.2, x=2.48832, y=1.25773







, approximately.



Edwin
 

Answer by ikleyn(52794)   (Show Source): You can put this solution on YOUR website!
 .


You are given two equations (system of two equations)


     = 5        (1)

     = y        (2)



Divide equation (1) by equation (2).  You will get


     = .      (3)


Apply the change-of-base formula for logarithms to the left side of equation (3).  Instead of equation (3), you will get then


     = .      (4)



It means that


    x = y^(5/y).        (5)


It is the sough expression of x via y,  with parameter  "a"  .


Expression (5) is your answer.   It allows calculate the value of x for any given positive value of y.




Solved and thoroughly explained.







///////////////







My comment after solving the problem:





    (1)  The problem is  .


         It asks  " Find the value of x. "

         But in this problem, there is no a unique single specific "value of x"
            and,  THEREFORE,  there  is  NOTHING  to  FIND  in this sense.

         There are infinitely many values x and y satisfying given equations.


    (2)  The correct formulation of the problem should be


            +--------------------------------------------------+
            |    Exclude parameter "a" from given equations    |
            |         and express x as a function of y.        |
            +--------------------------------------------------+


         It was EXACTLY what I did in my solution.






 

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