Compute $\lim_{x\to0} \ln^x(x)$ 
$$\lim_{x\to0} \ln^x(x)$$

I know I can use L'Hospital and get an answer equal to one.
But how can he ask a question like this even if the function is not continuous from $[0, 1]$. It has only discrete solutions not a graph

Note that $f(x)=\ln^x(x)$ is defined when both the following conditions are fulfilled


*

*for existence of $\ln x$ we need $x>0$

*for existence of $a^x$ we need $\ln x>0 \implies x>1$
therefore the given function is defined for $x>1$ and therefore the limit for $x\to 0$ is meaningless.
