What is the solution for $a^x + bx = c$?

Question

What is the solution for $a^x + bx = c$? Also, can anyone refer me to a good article/book/etc that covers general solution methods for exponential functions?

Thanks,

Answer 1

This can be solved in terms of the Lambert W function, which is defined as the solution for $w$ to $z = w e^w$. I think you'd read about the Lambert W function in a book or chapter with a title like "special functions" that just listed a lot of these various functions that can be used in weird circumstances like this, but I've never actually read one myself because I've never had any need to.

http://en.wikipedia.org/wiki/Lambert_W_function