Limiting the size of system.log and exception.log files

http://linux.die.net/man/8/logrotate

Follow this i think it will help you to solve your issue :-

cd /etc/logrotate.d/
vim magento-logrotate.conf

now add the following to the magento-logrotate.conf file:

/path/to/magento/var/log/*log {
rotate 7
daily
compress
missingok
notifempty
}

execute your configuration now:

logrotate -f /etc/logrotate.d/magento-logrotate.conf

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