I think it's almost silly to admit "log in" has the correct meaning and then quibble about the orthography. I'd contend that it very much is a verb in the same vein of phrasal and separable verbs as found in, e.g., German and English. The fact that to log and to login are different is curious enough. If I were a betting man, I'd say this is part of a lexical entry that composes the verb, and being non-finite, is left in its generated position as the finite portion becomes tensed. Regardless, usage trumps all.