I've seen different questions related to the same verb, but those questions implicate an imperative form (For example when you tell somebody to log in/on) which I think may vary the condition in which the verb is used.
He uses another program to log in to the system.
He uses another program to log into the system.
He uses another program to log on to the system.
He uses another program to log onto the system.
I think number 2 is correct but I'll wait for your suggestions.