The console logs some information to the central log, but most information is only logged if the console is started with the -D option to enable debug logging. The -D option accepts a single argument which controls the amount of logging to generate. It varies from 1 (least) to 9 (most). By default, the logging information is only written to stderr, but it can also be redirected to a file using the -f option, for example:
bash-2.05# ./startconsole -D 7 -f /tmp/console.log