I typed in the code just as the book asked and in for each cycle in the activity i wrote

public void onStart()
{
super.onStart();
Log.d(tag,"In the onStartEvent()");
}

...etc for (onRestart(), onResume(),....)

i properly imported the Log class even if it might not have been necessary and i have no errors

*The problem is when i start the application i don't see the output "In the onStartEvent()"

You need to put Eclipse in the "Debug" view
After the app is up and running, there is a button on the top right corner that says "Debug" next to the "Java" button. Click on the "Debug" button. This should bring you to the debug view. You should now see a "LogCat" window pane.

If not, you can try in Eclipse:
Window --> ShowView --> LogCat