I was working on a user manual and I want to write that a particular action would result in user being logged out of the system. I'm wondering whether the sentence should be "The action would log the user out of the system" or "the action would log out the user from the system".
The action would log the user out of the system
reads well (assuming "the action" is clear from the context) and I don't think it is particularly awkward.
The action would log out the user from the system
does not look right to me. To illustrate the point, consider this parallel construction:
The fence will keep the fox out of the henhouse.
The fence will keep out the fox from the henhouse.
The first line reads well but the second line does not.
This question might be helpful -- it is a discussion of variations of login and log in.
Grammatically, "log out" is a phrasal verb. Paul Brians' excellent Common Errors in English Usage has a detailed description and many examples.
Also (and I realize this part is not really an answer), you could consider rephrasing the sentence to avoid awkwardness. For example, it might be possible to say something like "The action would terminate the user session" or something like that.