If you're using Apache web server you can customize log output with LogFormat directive.
You can modify the access log with LogFormat. You cannot modify the error log.
From http://httpd.apache.org/docs/2.0/logs.html#errorlog :
It is not possible to customize the error log by adding or removing information. However, error log entries dealing with particular requests have corresponding entries in the access log. For instance, the above example entry corresponds to an access log entry with status code 403. Since it is possible to customize the access log, you can obtain more information about error conditions using that log file.