TITLE: Show that, for $t>0$, $\log t$ is not a polynomial.
QUESTION [9 upvotes]: How can I show that? I've tried to reverse the logarithm to it's exponential form in a trial to show that but I got no success. Can you help me?

REPLY [2 votes]: If $\log(t)$ is a polynomial, its derivative $\frac{1}{t}$ also is. But this is clearly impossible (the only invertible polynomials are constants because of the degree).