So you are giving a natural number $p$ and you are told to:
Find $x$ in $x!=p?$
What would you do?
Me: I take the $\log$ and I get: $\sum_{i=1}^{x}\log i=\log p$. and I get stuck there. You:?
Thanks.
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You could get an approximation for $x$ by computing: $$\int_1^x \log(\tau) d\tau = x\log(x)-x +1= \log(p)$$ Which may or may not be easier. – Joel May 27 '14 at 19:12
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Divide by $2,3,4,...$ – copper.hat May 27 '14 at 19:13