When you have an ajax call, it's extremely difficult to get a log from inside of the callback function. But if you enable the debugging
define('WP_DEBUG', true);
and then after that add
ini_set('log_errors',TRUE);
ini_set('error_reporting', E_ALL);
ini_set('error_log', dirname(__FILE__) . '/error_log.txt');
you will have an error.log.txt
file in your root folder where all your logs are located. you can even log them with
error_log( print_r( 'what I want to check goes here', true) );
inside your code. This will make your life a lot easier.