Solving Equations of the Form ln(x) = f(x)

[nunchakula]

Just came across this for a program I'm writing. I need to be able to solve an equation of the form ln(x) =f(x) where f isn't a logarithm. specifically, it's ln(x)=-x^2+ a*x+b.

Is this solvable for x or do I need a numeric approximation?

 

[alespa07]

Hello.

You must use a numerical approximation to solve this equation.

Bye.

 

[CRGreathouse]

It may be possible with the W-function, but I'd suggest numerical methods (Brent's method or the cosecant method).