Help! Totally stuck up with this limit.. I don't even know where to start with this
$$\displaystyle\lim_{x \rightarrow \frac{\pi}{6}} (2+\cos {6x})^{\ln |\sin {6x}|}$$
Please help me out (Hints in the right direction would be appreciated)

When $f(x)\to1$ and $g(x)\to\infty$ then in order to find $\lim f(x)^{g(x)}$, first find $\log\lim f(x)^{g(x)} = \lim\log(f(x)^{g(x)})= \lim(g(x)\log f(x))=L$ and conclude that $\lim f(x)^{g(x)}=\exp L$.
In this case you I'd try L'Hopital's rule applied to $\dfrac{\log f(x)}{1/g(x)}$.
