Solving a limit without reaching an indeterminate expression Find the limit of :
$$\lim\limits_{x \to 0^+}{(2\sqrt{x}+x)^\frac{1}{\ln x}}{}$$
I've tried to make it look like an exponent of e:
$$e^\frac{\ln (2*\sqrt{x}+x)}{\ln x}$$
but, then again I reach an indeterminate form of infinity divides by infinity.
I then tried to use L'Hospital's rule, which also seems not to work.

L'Hospital is not necessary.
$$(2\sqrt x+x)^{1/\ln x}=(2+\sqrt x)^{1/\ln x}\sqrt x^{1/\ln x}.$$
The first factor tends to $(2+0)^0=1$, and the second to $e^{\ln x/2\ln x}=\color{green}{\sqrt e}$.
