If $x$ and $y$ are both positive, evaluate

$\displaystyle \lim_{p\rightarrow 0}\frac{\ln(0.2\, x^p + 0.8\, y^p)}{p} =$

and $\displaystyle \lim_{p\rightarrow 0}(0.2\, x^p + 0.8\, y^p)^{{1}/{p}} =$