Hi didn't really know where this belongs so here goes...
show that $\displaystyle log_eN^c=O(N) \forall c \in \mathbb{R}\setminus{0}$
and
find O(f(x)) for $\displaystyle f(x) = x^4 + 2^x + log_en$
Thanks a lot for the help all=)
$\displaystyle \log(N^c)=c\log(N)$
Then as $\displaystyle \log(N) \in O(N)$, so is $\displaystyle c\log(N)$.
If you need to prove that: $\displaystyle \log(N) \in O(N)$
you use L'Hopital's rule to show that:
$\displaystyle \displaystyle \lim_{N \to \infty} \frac{\log(N)}{N}=0$
and the result follows from that.
CB