Allow multiple logging::LogMessage{Handler,Listener}s

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 201c7ba77cf9df592ece0827b0a17e79bfcbaa82..f90a77d891830ee2a310e8bd5be5ae7d5914a5f1 100644
--- a/remoting/host/native_messaging/log_message_handler.h
+++ b/remoting/host/native_messaging/log_message_handler.h
@@ -15,22 +15,26 @@
 
 namespace remoting {
 
-// Helper class for logging::SetLogMessageHandler to deliver log messages to
+// Helper class for logging::LogMessageHandler 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 {
+class LogMessageHandler : logging::LogMessageHandler {
  public:
   typedef base::Callback<void(std::unique_ptr<base::Value> message)> Delegate;
 
   explicit LogMessageHandler(const Delegate& delegate);
-  ~LogMessageHandler();
+  ~LogMessageHandler() override;
 
   static const char* kDebugMessageTypeName;
 
+  // logging::LogMessageHandler
+  bool OnMessage(int severity,
+                 const char* file,
+                 int line,
+                 size_t message_start,
+                 const std::string& str) override;
+
  private:
-  static bool OnLogMessage(
-      int severity, const char* file, int line,
-      size_t message_start, const std::string& str);
   void PostLogMessageToCorrectThread(
       int severity, const char* file, int line,
       size_t message_start, const std::string& str);
@@ -41,7 +45,6 @@ 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_;
 };