Move test_logging over to doctest.

Thanks to Christopher White from GHOP.
diff --git a/Misc/ACKS b/Misc/ACKS
index d209ec0..8c03784 100644
--- a/Misc/ACKS
+++ b/Misc/ACKS
@@ -704,6 +704,7 @@
 Cliff Wells
 Rickard Westman
 Jeff Wheeler
+Christopher White
 Mats Wichmann
 Truida Wiedijk
 Felix Wiemann
diff --git a/Misc/NEWS b/Misc/NEWS
index c8c4a03..940c3d6 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -1341,6 +1341,8 @@
 Tests
 -----
 
+- Refactor test_logging to use doctest.
+
 - Refactor test_profile and test_cprofile to use the same code to profile.
 
 - Make test_runpy reentrant by fixing _check_module to clear out any module