Limit of logarithm function I am trying to find $\lim_{x\to\infty}(\ln(a+x)-\ln(a-x))$. But I am having a little difficulty to get the solution.
What I did so far was rewrite the expression as $\lim_{x\to\infty}\ln((a+x)/(a-x))$ and as x goes to infinity I get $\infty/\infty$. If I use L'Hospital I get $\ln(-1)$ which is impossible. So can anyone help me please?
Thanks.

Assuming that $a$ and $x$ are real, you the consider the limit, when $x$ goes to infinity, of $$\log \left(\frac{(a+i x)^2}{a^2+x^2}\right)$$ which is, almost as you noticed,$\log \left(i^2\right)=2 \log (i)$. And $\log (i)=\frac{i \pi }{2}$. So, the limit is $i \pi$.  
Have a look at http://en.wikipedia.org/wiki/Complex_logarithm
