The log scope comes with several commands -- see Log Scope for a full list.
For example, if you want to debug something, you might want to run the following commands:
... do something ...
Note that the log levels set using the log:set commands are not persistent and will be lost upon restart. To configure those in a persistent way, you should edit the configuration file mentioned above using the config commands or directly using a text editor of your choice. The log commands have a separate configuration file: <RuntimeContainerPath>/etc/org.apache.karaf.log.cfg.
For more information about the logging system, see the site http://karaf.apache.org/manual/latest/#_log.