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Pretty much what the title says. To be more general, try to solve $x! = n$. I have tried for many hours and only ended up with a headache, is there any good/decent/practical way of solving such an eqation? I could not find anything about this on the internet.

Tl;dr What would be an exact solution for x, when x! = n?

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    You may need a table of values for the gamma function. – 2017-02-20
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    Similar question that might help here : http://math.stackexchange.com/q/18362/181463 – 2017-02-20

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The Gamma function generalizes factorials. For this particular numerical question you can ask Wolfram Alpha to $$ \text{ solve } x! = 10 $$

It tells you $$ x ≈ 3.39008 $$ which makes sense: it's between $3$ and $4$.

https://www.wolframalpha.com/input/?i=solve+x!+%3D+10

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Do you know about Gamma function that extends notion of factorial to all real and complex numbers? In general case the answer can be given only via it.

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    This doesn't tell you how to find the inverse though. – 2017-02-20
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    Even if it's hard to tell precise in analytic terms about its inverse for any particular argument you may try to find it numerically, check this MathOverflow question for more details: https://mathoverflow.net/questions/12828/inverse-gamma-function – 2017-02-20
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    This is definitely what Ethan Bolker done in his answer -- use CAS for solving numerically equation with Gamma function. I believe this is the only possible way. – 2017-02-20
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    Yes, but you haven't explained any of that! – 2017-02-21
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    Your post would be better provided as a Comment, as you provide less of an answer than a proposed limitation on *how* it can be answered (similar to comments offered about the same time). – 2017-02-21