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I tried to include several versions of the misspellings

How about Logon (Log on) instead of Login (Log in)?

I never really knew which was what was why.

I think it makes more sense for "log in" - there's even a site explaining why: http://loginisnotaverb.com/

Basically, only "log in" makes sense as a verb (because could you say you "logined"?). Although as a noun, it's okay.