File rsyslog-cloud-init.cfg of Package cloud-init.28546

# Log cloudinit generated log messages to file
:syslogtag, isequal, "[CLOUDINIT]" /var/log/cloud-init.log

# comment out the following line to allow CLOUDINIT messages through.
# Doing so means you'll also get CLOUDINIT messages in /var/log/syslog
& stop