The IBM Service log contains both the applications server messages that are written to System.out stream and special messages that contain extended service information that can be used to analyze the problem.
The IBM Service log is maintained in a binary format, so in order to view the activity.log file you will have to use either the command line based showlog tool that is shipped with WebSphere Application Server or use GUI based Log Analyzer tool that is shipped with WebSphere Application Server Toolkit.
You generally don't use this service log (activity log). Also you cannot redirect it to systemout. This log is mainly used for troubleshooting and If you are collecting logs and traces for any PMR, then it is required.