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