complex equation with exp-function and ln

[maryhann2007]

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

[VBAhack]

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.

[maryhann2007]

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

[maryhann2007]

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

[VBAhack]

Glad you were able to solve it.