Can I get a help on how to get write permission for a regular user?
I think your problem is that the log has user write permission, it just so happens that the 'user' is root.
eg. ls -l /var/log/some_log
-rw-r----- 1 root adm 4031 Mar 3 12:26 /var/log/some_log
As you can see, 'root' (the user) has read and write permission, 'adm' (the group) has read perm., and no else has any other perm.
I recommend you either use sudo to manage these logs:
or you make a special group to manage these logs, and add yourself to the group: