2
$\begingroup$

Suppose $a_1, a_2, ..., a_k\in\mathbb{R}$. Is it true that $f(x)=\sum\limits_{1 \leq i \leq k}{\dfrac{\pm a_i}{\log(1+a_ix)}}$ has at most finitely many zeros (on the domain where $1+a_ix>0$ for all $i$) for every sign combination? I have plotted several curves in Mathematica and feel it might be correct. Any ideas to prove it?

  • 0
    Thanks for the response. I have deleted my (now useless) answer and edited your question according to your explanation. Please see if I understand you correctly. If not, please feel free to roll back the question to an earlier version.2012-12-20
  • 0
    @user1551, thanks for the change. Just now I found a solution to this problem.2012-12-20

1 Answers 1