How can Newton's method be used to solve exponential equations iteratively?

[Gin]

Hi. I've been mulling over the problem of how to solve $$y=e^{ax}+e^{bx}$$ for x. I know it can't be solved numerically and have been trying to think of a way to solve it iteratively. The problem is, I can only find algorithms for polynomials and they don't seem to work for exponential problems. I'd rather not have to make an approximation for the exponential and was hoping someone might know an appropriate algorithm or have another means of approach.

 

[christianjb]

Try Newton Raphson root-finding method

x(n+1)=x(n)-f[x(n)]/f'[x(n)]

where f(x)=e^ax+e^bx-y

 

[Gin]

Hey thanks for that. I had tried Newton's method, but silly me messed up some simple numbers. I tried again and paid more attention and it worked. For some reason I thought that Newton's method wouldn't work for an exponential.