How to turn off application log in dev mode
Lifting from this answer to a similar question: 

You'll have to write a simple, custom plugin, and add the following to the init() method in your plugin's primary class:

craft()-&gt;log-&gt;removeRoute('WebLogRoute');
craft()-&gt;log-&gt;removeRoute('ProfileLogRoute');


For instant success, you can scaffold your plugin by visiting the plugin factory – name it whatever you want and don't enable any components.