Capture log messages via instrumentation

pkg/analysis_server/lib/src/analysis_logger.dart

Index: pkg/analysis_server/lib/src/analysis_logger.dart
diff --git a/pkg/analysis_server/lib/src/analysis_logger.dart b/pkg/analysis_server/lib/src/analysis_logger.dart
index 32a94171d1e4f0e12ae6da44513da55bcb71b8c0..e87bc2aaa99993ec84342b81be7c5177eb3c8277 100644
--- a/pkg/analysis_server/lib/src/analysis_logger.dart
+++ b/pkg/analysis_server/lib/src/analysis_logger.dart
@@ -18,6 +18,15 @@ class AnalysisLogger implements Logger {
    */
   final logging.Logger baseLogger = new logging.Logger('analysis.server');
 
+  AnalysisLogger() {
+    logging.Logger.root.onRecord.listen((logging.LogRecord record) {
+      AnalysisEngine.instance.instrumentationService.logLogEntry(
+          record.level.name,
+          record.time,
+          record.message);
+    });
+  }
+
   @override
   void logError(String message, [CaughtException exception]) {
     if (exception == null) {