support multiple log message handlers in base/logging.h

remoting/host/native_messaging/log_message_handler.h

Index: remoting/host/native_messaging/log_message_handler.h
diff --git a/remoting/host/native_messaging/log_message_handler.h b/remoting/host/native_messaging/log_message_handler.h
index 7c5cea08c1256471d4a47889fb17f0d7efa74b75..c8b3441e582c69ed49e0b8fb2567bdebdc27dc42 100644
--- a/remoting/host/native_messaging/log_message_handler.h
+++ b/remoting/host/native_messaging/log_message_handler.h
@@ -20,7 +20,7 @@ class SingleThreadTaskRunner;
 
 namespace remoting {
 
-// Helper class for logging::SetLogMessageHandler to deliver log messages to
+// Helper class for logging::AddLogMessageHandler to deliver log messages to
 // a consistent thread in a thread-safe way and in a format suitable for sending
 // over a Native Messaging channel.
 class LogMessageHandler {
@@ -46,7 +46,6 @@ class LogMessageHandler {
   Delegate delegate_;
   bool suppress_logging_;
   scoped_refptr<base::SingleThreadTaskRunner> caller_task_runner_;
-  logging::LogMessageHandlerFunction previous_log_message_handler_;
   base::WeakPtrFactory<LogMessageHandler> weak_ptr_factory_;
 };