By default Ubuntu logs cron results to:
/var/log/syslog
Should you want a dedicated Cron log you can do the following:
nano /etc/rsyslog.d/50-default.conf
Uncomment the following line:
#cron.* /var/log/cron.log
Restart rsyslog:
service rsyslog restart
Restart the cron daemon:
service cron restart