Logging PPPoE

I want to buy any nighthawk Router and I have a question:

My Attachement: PPPoE to DSL provider Modem.

If you disconnect wan cable, and connect again (or restart your modem). and router re-established wan connection ...

Will this event be logged in router logs ? How ? (please cut & paste)

I want to be noticed if provider drops or if establishment fails (Cause "no carrier" and so on)

Thanking you in anticipation / rudolf