Question

lim x-->infinity (lnx)^(1/x)

Answer 1

Let f(x) = (ln x)^(1/x)

What's the limit of ln(f(x)) ?

Answer 2

i didn't get your question..

Answer 3

I'm suggesting a strategy. Instead of trying to find the limit of the function directly, try and find the limit of the log of the function
g(x) = ln( f(x) )

Answer 4

James can you always do that, or only at times like l'hospital?

Answer 5

provided the limit of ln( f(x) ) exists, you can do it. That is just like l'Hopital's rule. You need the limit of the new expression to exist and then it can be used to write down the limit of the original