complex equation with exp-function and ln

Hello,

I will be glad of every clue to solve this equation.

a/(12*d*x)+(b*c)/(1+exp(c*x))=(b/d)*ln(1+exp(-c*x)

a, b, c, d are constants and I'm looking for x.
It is really complex equation and I've tried everything.

Thanks for any help.

Mary

Welcome to the forums.

Are you sure it is solveable algebraically?

A lot of equations don't have closed form solutions, even simple ones. A couple of examples are 5 = x^x or 3x = e^x, though I'm not 100% sure about the 2nd example. You may need to resort to graphing and/or numerical methods. :)

Thank you for the answer. I will try to solve this equation in other way. The second equation, which you mentioned, is solvable, i.e. x=-lambertw(-1/3).

Mary

The first equation is also solvable, and the solution is following:
x=log(5)/lambertw(log(5)).

W = LAMBERTW(X) is the solution to w*exp(w) = x and Lambertw function is included in C-language.

Mary

Glad you were able to solve it. :)