Q. Is the term “log in to” or “log into” when a user is connecting to a computer?
A. Though the right answer depends on a subtle distinction that’s often overlooked (with, let’s be honest, no significant loss of meaning), formally correct usage would call for “log in to” (with “in to” as two words). The same goes for logging on—or signing in or signing on—to something. In each case, the word “in” (or “on”) forms a part of the verb phrase, where it functions as an adverb rather than as a preposition. For some additional considerations, see CMOS 5.250, under “onto; on to; on.”