Move test_logging over to doctest.

Thanks to Christopher White from GHOP.
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