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**centenial** I'm having trouble with this proof:

Show that if $\displaystyle p(n)$ is a polynomial in $\displaystyle n$, then $\displaystyle \log{p(n)}$ is $\displaystyle O(\log{n})$.

I'm given this definition for O(n):

$\displaystyle T(N) = O(f(N))$ if there are positive constants $\displaystyle c$ and $\displaystyle n_0$ such that $\displaystyle T(N) \leq cf(N)$ when $\displaystyle N \geq n_0$.

I'm not sure how to use it to arrive at the conclusion that $\displaystyle \log{p(n)} = O(\log{n})$. Wouldn't $\displaystyle \log{p(n)}$ always be greater than $\displaystyle \log{n}$?

Any help would be much appreciated,