$ \displaystyle\lim_{x \to 0^+} \frac{1+lnx^7-lnx^3}{1+lnx^2+lnx^3} = $
$ \displaystyle\lim_{x \to 0^+} \frac{1+7lnx-3lnx}{1+2lnx+3lnx} = $
dividiamo sopra e sotto per ln x
$ \displaystyle\lim_{x \to 0^+} \frac{\frac{1}{ln x}+7-3}{\frac{1}{ln x}+2+3} = \frac{4}{5}$