People out there seriously think "login" is a verb? Why make things complicated? You just forgot the space. The usage of the verbs "log" and "sign" (as in "log in" and "sign in") is clearly a metaphor for the paper forms ("logs") used for buildings, equipment cabinets, etc.

Here's a visual aid: http://www.flickr.com/photos/riggzy/3177839298/

Also see meanings 6 and 13 at http://dictionary.reference.com/browse/log.