Solution 1:

CRON delivers the applications' output (stdout, stderr) via local mail. Ubuntu apparantly does not have an MTA (Mail Transfer Agent) installed by default these days. CRON prints a notification into the systems logfile whenever a delivery failed:

Jul  5 11:38:01 ip-10-70-75-234 CRON[4970]: (CRON) info (No MTA installed, discarding output)

You can install an MTA, e.g. postfix, for internal (local) use only, e.g.

aptitude install postfix

During the installation you will be asked what default configuration to use. You should select the Local only configuration.

Thereafter you can find the output of the applications ran by CRON using

tail -f /var/mail/<your_username>

Of course you can also write the logging output to a dedicated log file or pipe/redirect the output to a file by using built-in shell functionality...