Help me finish finding this limit.

lim (1-2x)^(1/x) (reads (1-2x) to the 1 over x
x->0

1. set y = (1-2x)^(1/x)
2. take ln of both sides :
lny = ln(1-2x)^(1/x)
simplify
lny = (1/x)(ln 1-2x)
lny = (ln(1-2x)) / x
3. seeing if i do limits it is 0/0 i can use l'hopitals rule and take derivatives
lny = -2 / ln(1-2x)

now using x->0 i get -infinity, but thats not the answer, i must be missing a step, not sure what to do next...

lny = (ln(1-2x)) / x
when you use l'hopital's rule, you get:
[1/(1-2x)](-2)/1 =
-2/(1-2x)

So now plug in 0 for x:
-2/(1-0) = -2/1 = -2
So lny = -2
So e^(-2) = y
so you answer is 1/(e^2)


hope this helps! :)