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%L_c \sim \left[\frac{V}{2\,f_l\, f_i\, f_c}\right]^{1/4}.  %\end{equation}  Since we are discussing the second hypothesis, $f_i$ is not a small number. Let's assume, as Frank Drake did in his estimates, that $f_1=1$. $fi=1$.  We obtain %On the other hand our discussion of the Drake equation led to the conclusion that, roughly speaking, $N \sim L$ %(meaning the denominator in previous equation is $\sim$ 1) (but see the \href{http://en.wikipedia.org/wiki%%/Rare_Earth_hypothesis}{rare Earth hypothesis} for a different conclusion). Therefore we can further simplify and %obtain   \begin{equation}  %L_c \sim \left(\frac{V}{L_c}\right)^{1/3} = V^{1/4}