diff --git a/src/backend/libpq/auth.c b/src/backend/libpq/auth.c
index 0356fe3e454..81dabb9c273 100644
--- a/src/backend/libpq/auth.c
+++ b/src/backend/libpq/auth.c
@@ -645,6 +645,22 @@ ClientAuthentication(Port *port)
 #endif
 	}
 
+	if (Log_connections && status == STATUS_OK &&
+		!MyClientConnectionInfo.authn_id)
+	{
+		/*
+		 * Normally, if log_connections is set, the call to set_authn_id()
+		 * will log the connection.  However, if that function is never
+		 * called, perhaps because the trust method is in use, then we handle
+		 * the logging here instead.
+		 */
+		ereport(LOG,
+				errmsg("connection authenticated: user=\"%s\" method=%s "
+					   "(%s:%d)",
+					   port->user_name, hba_authname(port->hba->auth_method),
+					   port->hba->sourcefile, port->hba->linenumber));
+	}
+
 	if (ClientAuthentication_hook)
 		(*ClientAuthentication_hook) (port, status);
 
diff --git a/src/test/authentication/t/001_password.pl b/src/test/authentication/t/001_password.pl
index 12552837a8e..891860886af 100644
--- a/src/test/authentication/t/001_password.pl
+++ b/src/test/authentication/t/001_password.pl
@@ -136,13 +136,13 @@ SKIP:
 # Create a database to test regular expression.
 $node->safe_psql('postgres', "CREATE database regex_testdb;");
 
-# For "trust" method, all users should be able to connect. These users are not
-# considered to be authenticated.
+# For "trust" method, all users should be able to connect.
 reset_pg_hba($node, 'all', 'all', 'trust');
 test_conn($node, 'user=scram_role', 'trust', 0,
-	log_unlike => [qr/connection authenticated:/]);
+	log_like =>
+	  [qr/connection authenticated: user="scram_role" method=trust/]);
 test_conn($node, 'user=md5_role', 'trust', 0,
-	log_unlike => [qr/connection authenticated:/]);
+	log_like => [qr/connection authenticated: user="md5_role" method=trust/]);
 
 # SYSTEM_USER is null when not authenticated.
 $res = $node->safe_psql('postgres', "SELECT SYSTEM_USER IS NULL;");
diff --git a/src/test/ssl/t/001_ssltests.pl b/src/test/ssl/t/001_ssltests.pl
index 76442de063f..23248d71b06 100644
--- a/src/test/ssl/t/001_ssltests.pl
+++ b/src/test/ssl/t/001_ssltests.pl
@@ -800,8 +800,8 @@ $node->connect_ok(
 	"$common_connstr user=ssltestuser sslcert=ssl/client.crt "
 	  . sslkey('client.key'),
 	"auth_option clientcert=verify-full succeeds with matching username and Common Name",
-	# verify-full does not provide authentication
-	log_unlike => [qr/connection authenticated:/],);
+	log_like =>
+	  [qr/connection authenticated: user="ssltestuser" method=trust/],);
 
 $node->connect_fails(
 	"$common_connstr user=anotheruser sslcert=ssl/client.crt "
@@ -818,8 +818,8 @@ $node->connect_ok(
 	"$common_connstr user=yetanotheruser sslcert=ssl/client.crt "
 	  . sslkey('client.key'),
 	"auth_option clientcert=verify-ca succeeds with mismatching username and Common Name",
-	# verify-full does not provide authentication
-	log_unlike => [qr/connection authenticated:/],);
+	log_like =>
+	  [qr/connection authenticated: user="yetanotheruser" method=trust/],);
 
 # intermediate client_ca.crt is provided by client, and isn't in server's ssl_ca_file
 switch_server_cert($node, certfile => 'server-cn-only', cafile => 'root_ca');