Confluence sends its log output to standard out, so by default Weblogic does not record it.

To redirect Confluence's log output to a file follow these instructions Redirecting System.out and System.err to a File.

(info) From Confluence 2.7, logging will be to the application server logs until Confluence has completed its initial bootstrap. Then all logging will be to <confluence-home>/logs/atlassian-confluence.log. See Working with Confluence Logs.