I am trying to solve

((1 - x)/(x*Z))^x* A^x*B^(1 - x) == M

where x is constrained to the interval [0,1] and all other values (A,B,M and Z) are positive real constants. I can find numerical solutions using NSolve, but am wondering if an analytical solutions might be possible on the bounded domain [0,1]?

  • $\begingroup$ is xZ one variable? $\endgroup$
    – Nasser
    Commented Apr 27, 2020 at 20:11
  • $\begingroup$ It's x*Z. Sorry, can't figure out how to display it correctly. $\endgroup$
    – Hunt
    Commented Apr 27, 2020 at 20:45

1 Answer 1


The syntax you would probably want to use is the following:

Assuming[{{A, B, Z, M} ∈ PositiveReals}, 
 Simplify[Solve[((1 - x)/(x Z))^x* A^x*B^(1 - x) == M && x > 0 && 
    x < 1, x]]]

I have not been able to find an analytical solution to this though. You can try leaving it running all day if you want. But I'd safely say there isn't one.


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