Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I am trying to prove that if ${s_n}$ is a convergent sequence, $\lim_{ n \to \infty} s_n = s$ iff $\lim_{ n \to \infty} \log(s_n) = \log(s)$. I don't have any notion of continuity yet (although I know that continuous functions are precisely the ones that preserve limits), so i am trying to do this without that fact. This is part of a larger problem where i have a sequence $s_n$ which i am trying to show converges to 1, but so far i managed to show $log(s_n)$ converges to $0$.

share|cite|improve this question
The fact that the logarithm function is monotone should come in very handy. So should the fact that $\lim_{n\to\infty} x^{1/n}=1$ whenever $x>0$, I think. – Harald Hanche-Olsen Nov 14 '12 at 8:57
Well, what definition of $\log$ are you using? – Rahul Nov 14 '12 at 10:16
Mike: Maybe by looking at how you got to log(s_n) --> 0 you can "work backwards" and see how to actually get s_n --> 1 on reversing the steps. – coffeemath Nov 14 '12 at 18:17

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.