The log outputs are stored by default in the server application standard log file (STDOUT) as defined in the Log4j.xml file located in the <ApplicationPath>/WEB-INF/classes folder. However you can store the log in a different file by setting the path to this file in the Log4j.xml file.
To do so, simply set the path in the Configuration page in Talend Administration Center.
For more information, refer to your Talend Administration Center User Guide. If you leave the path field blank in the Configuration page, then you can also customize the Log4j.xml to address your custom needs.