For some continuous function $\displaystyle f:\mathbb{R}\rightarrow \mathbb{R}$, if I know the value of $\displaystyle \frac{f'(x)}{f(x)}$ at some point $\displaystyle x=a$, does that tell me any information about thevalueof either $\displaystyle f'(a)$ or $\displaystyle f(a)$?

I'm doubting it, but I want to make sure. Say for example I knew that this ratio was irrational. Does that tell me anything about the rationality of $\displaystyle f'(a)$ or $\displaystyle f(a)$?