If you wish to send output of cronjobs to syslog instead of email use the following:
20 10 * * * /opt/script/dostuff.py 2>&1 | /usr/bin/logger -t stuffdoer
If you want live-updates in the log file it can be necessary to unbuffer it, install the “expect” package and modify the command like so:
20 10 * * * /usr/bin/unbuffer /opt/script/dostuff.py 2>&1 | /usr/bin/logger -t stuffdoer
If it’s a python script you can accomplish the same thing by adding “-u” to the shebang.