Question 1194342
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<pre>

You are given two equations (system of two equations)


    {{{log(a,(x))}}} = 5        (1)

    {{{log(a,(y))}}} = y        (2)



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


    {{{log(a,(x))/log(a,(y))}}} = {{{5/y}}}.      (3)


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


    {{{log(y,(x))}}} = {{{5/y}}}.      (4)



It means that


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


It is the sough expression of x via y,  with parameter  "a"  {{{highlight(excluded)}}}.


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

Solved and thoroughly explained.



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My comment after solving the problem:


<pre>
    (1)  The problem is {{{highlight(posed)}}} {{{highlight(incorrectly)}}}.


         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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