Ubuntu syslog does not show previous days's logs

My Cron job is not running and i want to see what's problem in the syslog.

But that log is only showing current date only ,

Is there any way to keep logs for the last 10 days?

The logs are most likely being rotated by the logrotate process. Look in /etc/logrotate.conf. You should see something like this:

daily

rotate 1

Change that to:

daily

rotate 10

You could also do something like this to keep 4 weeks of logs:

weekly

rotate 4

Yesterdays log is /var/log/syslog.1. They are rotated daily about 6 in the morning. Previous days logs are syslog.2.gz... Use zless or zgrep to look at the compressed logs.

Data is likely in /var/log/messages as well. This is rotated weekly, and has four weeks of old logs.