This is probably unnecessary complexity..consider what happens when log files rotate.  It's probably fine to just pick up the file where it is at open time and follow from there.  Otherwise, you could add a defaulting parameter that allows callers to pass in the offset they need.  I say if some behaviour isn't central/key to the class's subject, just leave it as an extension point - in other words, there's rarely a need to solve all problem aspects in the first-go.  It's okay to leave bits to be added later.