I put my program in startup applications because of this. The directory /var/log is taking around 36 GB space.
Can I delete syslog and syslog.1 file which are taking the highest percentage of storage in /var/log directory?
Of course you can...
But... normally, on a default Ubuntu, the system will clean up logs automatically using something called logrotate. By default it will logrotate daily (You can see that in /etc/logrotate.d/rsyslog)
Since they did become so large, you may want to see what is causing the log to become so incredibly large in less than 24h... There might be a significant problem, like a disk having a lot of errors. Perhaps take a look at the contents in real time for a while. To do that:
tail -f /var/log/syslog
To get back to your prompt, hit Ctrl-C.