It would be much more traffic (and execution time) friendly, if you put pipe and grep to "" as well, so grep would be executed on remote server and ssh won't have to send the entire log to your machine.
And I'd like to highlight the overwhelming awesomeness of ~/.ssh/config file. If you haven't heard about it or use shell alias instead please please read about it. It supports autocomplete, dynamic paths to key files and many other cool things which can make your ssh client experience simply great.