Depending on your DB structure, there is no real purpose of logging the password they logged in with, because it can be inferred that if the logged in, then the used the current password :)
If you have a history of password changes (and obviously, storing the password in a hashed format so it can't be reversed anyway) you can rely on this system completely, to determine, if for some reason it's ever required, that they did indeed use password X, that they had between Date FOO and Date BAR.
Anyway, the point is, user X logged in.
is all that really needs to be logged.