But there is no reason why a configurable library can't have reasonable default behavior if no configuration is supplied. While still being configurable. If you're winding up as a buried dependency that end developers may not be aware of or care about, you want to do this.
That way the console can tell you about configuration errors, and by default the library will log nothing. If the library author considers it important to log somewhere, the library author is responsible for putting both an understandable warning up, and writing documentation.
If you are creating a console application? Stderr is the standard way to log errors. Let the user decide if where it points to.
If you are creating a daemon, set the log destiny at the launch script. The application can either log to stderr anyway and let the script handle everything, or offer a parameter for setting the log channel.
The Java community fixation on logging is really not deserved. It's more caused by bad error handling by their main web servers than by any fundamental problem.