This is by design because appending logging to ajax response may ruin your ajax behavior. You can set showInFireBug=true for the CWebRoute so that the logging output is displayed in FireBug console (for both normal and ajax responses)
but unless I'm mistaken all log messages are written at the end of the application cycle, when I use an action through ajax this app cycle does not fully complete so no log messages are written (even with firebug option)
juste tested it again and calling an action with a call to :
Yii::trace('test');
write 'test' in the firebug console with a normal call through browser url
but not through an ajax call
I would think that it would be very convenient to log to a file or to firebug even when requesting an action through ajax