Where are Magento's log files located?

You can find them in /var/log within your root Magento installation

There will usually be two files by default, exception.log and system.log.

If the directories or files don't exist, create them and give them the correct permissions, then enable logging within Magento by going to System > Configuration > Developer > Log Settings > Enabled = Yes

To create your custom log file, try this code

Mage::log('your debug message', null, 'yourlog_filename.log');

Refer this Answer