I am evaluating the expression:

$\ln(1)$

And I know the trivial solution is $0$. 

Are there other solutions to this equation? I feel there should be, my logic is as follows:

if:

$\ln(1) = x \implies 1 = e^x \implies 1 = 1 + x + x^2/2! + x^3/3!... $
$\qquad\qquad\qquad\qquad\qquad\implies 0 = x + x^2/2! + x^3/3!...$

$\implies x = 0$ is one solution, the other solution is all $x$ such that: $$1 + x/2! + x^2/3! + x^3/4! ... = 0$$

There have to be other solutions, or limiting solutions...

What are they?