Limit of logarithm of square roots function

[salparadise]

Homework Statement

I need to prove that the following limit holds when

$$\sqrt{s}>>m$$

$$\log\left(\frac{\sqrt{s}+\sqrt{s-4m^2}}{\sqrt{s}-\sqrt{s-4m^2}}\right) \rightarrow \log\left(\frac{s}{m^2}\right)$$

The Attempt at a Solution

I've tried several manipulations using logarithms properties but had no success.

Thanks

 

[Mute]

You don't need to bother with the logarithm, just focus on the stuff inside. I'll give you a starting hint; you should provide the rest of your workings after that if you can't get it and want further help. To start, I would pull the factor of $\sqrt{s}$ out from the top and bottom of the fraction inside the logarithm. Find the limiting form of the fraction in your desired limit.

 

[salparadise]

Hello Mute, thanks for the help. I've managed to do it, after Taylor expansion of $$\sqrt{1-x}$$, where in my limit:

$$x=\frac{4m^2}{s}\rightarrow 0$$.

As I'm under some time pressure to finish this, very bigg, home exam I'm already not thinking so clearly..

Thanks again