while [ 1 ]; do sleep 1; clear; tail log.txt; done
This does not have the drawback of passing command and arguments to watch (sometimes you need to hop extra loops to make it correctly), and it clears the terminal.
watch
Use this command.
watch tail -n 1 log.txt
You can watch command to monitor the file changes/difference (-d) every n seconds
-d
n
watch -n 5 -d cat log.txt