[update_engine] Update to use not-hideously-old logging API from chrome

BUG=None
TEST=compile

Change-Id: Ieed8952b6806a72b59e16c1579f7293b6a98157a

Review URL: http://codereview.chromium.org/3170010
diff --git a/subprocess.h b/subprocess.h
index 7fd3052..6685f4d 100644
--- a/subprocess.h
+++ b/subprocess.h
@@ -10,7 +10,7 @@
 #include <vector>
 #include <glib.h>
 #include "base/basictypes.h"
-#include "chromeos/obsolete_logging.h"
+#include "base/logging.h"
 
 // The Subprocess class is a singleton. It's used to spawn off a subprocess
 // and get notified when the subprocess exits. The result of Exec() can