Hi all!

I have the following general equation which is: $\displaystyle s(s+t)=((1-t)s(x)^\alpha + ts(x+1)^\alpha)^\frac{1}{\alpha}$. where s is survival function

It is told to me that when I substitute $\displaystyle \alpha =0$, I will be able to obtain

$\displaystyle log(s(x+t))=(1-t)log (s(x))+(t) log (s(x+1))$.

But how do I do that since when $\displaystyle \alpha=0$, $\displaystyle 1/\alpha$ goes to infinity??