There are few solutions:
$ watch -n 1 tail -n 10 path/to/log/file
Note: to end watching press ctrl^c (ctrl+c)
-n 1causes refreshing once per second
-n 10causes reading 10 last lines from file
$ less +F path/to/file
Note: to end watching press ctrl^c (ctrl+c); to exit less program press q key.
It is possible to enable following for opened less program by pressing shift+f keys.