The number of times I've needed to check the papertrail logs for my Heroku-hosted Rails app is a lot. I open a browser tab, go through several layers of navigation to get to my app's dashboard, and then click the papertrail link under Add-ons.
There is a much quicker way using the Heroku CLI.
$ heroku addons:open papertrail -a my-app-name
Opening https://addons-sso.heroku.com/apps/abc123/addons/efg456...It sends you to an add-ons SSO link in the browser which authenticates you and drops you into the dashboard for that specific add-on. You just need to specify the add-on name and the app name.