The Collaborative International Dictionary of English v.0.48:

log in \log in\, log on \log on\, v. i. (Computers)
   To establish communication with a host computer from a
   terminal or remote computer.
   [PJC] Logistic

WordNet (r) 3.0 (2006):

log in
    v 1: enter a computer; "Have you logged in lately?" [syn: log
         in, log on, log-in] [ant: log off, log out]

The Free On-line Dictionary of Computing (30 December 2018):

log in

    (Or "login", "log on", "logon") To start a
   session with a system, usually by giving a user name and
   password as a means of user authentication.  The term is
   also used to mean the ability to access a service (also called
   an account), e.g. "Have you been given a login yet?"

   "Log in/on" is occasionally misused to refer to starting a
   session where no authorisation is involved, or to access where
   there is no session involved.  E.g. "Log on to our Web
   site!"

   "login" is also the Unix program which reads and verifies a
   user's user name and password and starts an interactive
   session.

   The noun forms are usually written as a single word whereas
   the verb forms are often written as two words.

   To end a session is to "log out" or "off".

   (2006-07-10)