To enable Logging, set debug_mode to true, then provide a path of a writable file on debug_file on your configuration file or hash:

array(
  "providers" => array ( /* .. */  ),

  "debug_mode"   => true ,

  // to enable logging, set 'debug_mode' to true, then provide here a path of a writable file
  "debug_file"   => "/temp/hybridauth.log",
);

There is three levels defined by HybridAuth Logger:

   INFO: Log a message at the info level.

   DEBUG: Log a message at the debug level.

   ERROR: Log a message at the error level.