""Log in" designates the action through which one may gain access to a service. You "log in" with your name and user password. "Log on" indicates not only the action of logging in but also the idea of using the service. It's really hard to explain, but when you say "I logged in" that could mean that you did that and then left, whereas "I logged on" implies that you logged in and stayed."
Consult the following link for more information.
login, log-in, log in
Hope this helps!!:)