## anonymous 4 years ago solve lim x->inf (ln x)^(1/x)

1. anonymous

getting 0

2. klimenkov

$\lim_{x\rightarrow\infty}(\ln x)^{\frac 1x}=1$

3. anonymous

start by taking the log get $\frac{1}{x}\ln(\ln(x))=\frac{\ln(\ln(x))}{x}$

4. anonymous

now that limit is pretty clearly 0, since log grows much slower than $$x$$ and the log of the log grows amazingly slowly since that limit is 0, and it is the limit of the log, you get $$e^0=1$$ and the limit of your original question

5. anonymous

ty