https://docs.oracle.com/cd/E23943_01/web.1111/e13739/logging_services.htm#WLLOG199

To redirect messages from JDK logging system to WebLogic standard log files we need to add special ServletLoggingHandler.

logging.properties:

# Specify the handlers to create in the root logger
handlers = weblogic.logging.ServerLoggingHandler

# Register handlers for the com.foo.toyshop and its child loggers
com.foo.toyshop.handlers = java.util.logging.ConsoleHandler, weblogic.logging.ServerLoggingHandler
 
# Do not send the toyshop log messages to the root handler
com.foo.toyshop.useParentHandlers = false
 
# Set the default logging level for the root logger
.level = ALL
 
# Set the default logging level for new ConsoleHandler instances
java.util.logging.ConsoleHandler.level = INFO
 
# Set the default logging level for new FileHandler instances
weblogic.logging.ServerLoggingHandler.level = ALL

We have to add the following argument for JVM to start using our properties file.

java -Djava.util.logging.config.file=C:\mydomain\logging.properties weblogic.Server

If we want to put our custom logging.properties into jar or war archive, we have to load it programmatically:

    private void initLogging() {
        InputStream inputStream = this.getClass().getResourceAsStream("/logging.properties");
        try
        {
            LogManager.getLogManager().readConfiguration(inputStream);
            System.out.println("Logging initialized");
        }
        catch (final IOException e)
        {
            Logger.getAnonymousLogger().severe("Could not load default logging.properties file");
            Logger.getAnonymousLogger().severe(e.getMessage() );
        }       
    }