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Here is a tip from jensgram:.
In “Homepage Usability”, Jakob Nielsen (together with Marie Tahir, 2002, p. 53) recommends the use of “sign in” / “sign out” over “log in” / “log out”.
This data is based on a survey of large websites.
But there are some other thoughts on the matter.
Rahul points out that Log in and Login are valid verbs and nouns while Signin is not.
Finally lukemh recommends that whatever you chose, just be consistent through your site or application.