# Finding solutions to $\frac{2 t }{x}= B_r \log B_r + B_s + B_s x \log(B_s x)$

Given $B_r$, $B_s$, $t$ being constants, and $x$ being a variable $0\leq x\leq 1$ how can I solve this equation?

$$\frac{2 t }{x}= B_r \log B_r + B_s + B_s x \log(B_s x)$$

If i plot the two functions I see that they intersect somewhere, so a solution must exist.

Thank you.

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What is $*$? is the multiplication? –  MphLee Apr 15 '13 at 10:21
Yes it is the multiplication –  Francesco Apr 16 '13 at 8:17

Mathematica refuses to solve the equation ("cannot be solved by the methods available"), so I highly doubt there will be any reasonable symbolic expression for $x$; I think your best bet is to resort to numerical approximation.
In that case I think the only option left is to define a new function $f(t, B_r, B_s)$, defined on a suitable domain, that returns the solution $x$ by definition. Perhaps you can then derive properties of this $f$ (e.g. its behaviour upon modifying the parameters). –  Lord_Farin Apr 15 '13 at 10:47