Number of solutions of exponential equation Can anyone tell me how to find number of solutions $(x+a)^x=b$? For example $(x+1)^x=-1$ has four complex solutions, $(x+3)^x=10$ has two solutions,one positive one negative, and $(x-4)^x=-10$ hasn't any solutions.
PS.Sorry for my bad English,I hope you understand my question.

Sorry, I don't understand. So, $a_0=1$,$c=-\ln b$,$r = -a$; But there is 1/x in  $\exp \left( \frac{1}{x}\log b \right)$and x in the left side of $e^{-cx} = a_o(x-r)$.
