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How fast does $\binom{n}{k}$, $n$ fixed, grow when $k \le n/2$?

Especially, I'm interested in the growth of the "inverse" of binomial coefficient $B_n(x) := \min \{k:\binom{n}{k} \ge x\}$.

EDIT: This was answered in a previous post, according to which $B_n(x) = O(\log x)$.

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    This seems to be a duplicate. Although note: I choose the wrong link when I voted to close.2012-01-31

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