Ironic that the instruction at the bottom of this page is 'Sign up or login'.
I'm here because I'm torn between log in to and log into and looking for clarification. At this point in time, I suspect the prevailing opinion is correct - that log in to is preferable for purposes of clarity.
However, I don't doubt that we will soon treat the process of logging in as a figurative point of entry, meaning that log into will make full conceptual sense (cf you don't physically delve into a problem or pile into an argument, yet both are correct grammatically because they are semantically [i.e. figurativelyfiguratively]).