Work adeventure : Permission to view sql error log (ONLY)

I had a situation where I had to give a user permission to view the sqlerror log only. I achieved by doing the following

• Create a login  DBA_error_logUser  in the server
• Added the login to the securityadmin server role ( to view sql error log the login must be the member of this server role)
• Created a user DBA_error_logUser  with map to the login to grant access to the error logs
• Deny Alter to any Login 
• Grant permission to view Sql Server Logs for the user
• Create a log on Trigger to deny access to Query Window

---Create a login  DBA_error_logUser  in the server

use [master]
GO

CREATE LOGIN [DBA_ErrorLogUser] WITH PASSWORD=N'123', DEFAULT_DATABASE=[master], CHECK_EXPIRATION=OFF, CHECK_POLICY=OFF GO


--Added the login to the securityadmin server role
EXEC master..sp_addsrvrolemember @loginame = N'DBA_ErrorLogUser', @rolename = N'securityadmin'
 GO


--Created a user DBA_error_logUser  with map to the login to grant access to the error logs

CREATE USER [DBA_ErrorLogUser] FOR LOGIN [DBA_ErrorLogUser] GO

--Deny Alter to any Login

DENY ALTER ANY LOGIN TO DBA_ErrorLogUser GO


--Grant permission to view Sql Server Logs for the user

Grant EXECUTE ON master.sys.xp_readerrorlog TO DBA_ErrorLogUser GO

--Create a log on Trigger to deny access to Query Window

  IF EXISTS ( SELECT * FROM master.sys.server_triggers
                WHERE parent_class_desc = 'SERVER' AND name = N'Deny_QueryWindowLogin_Trigger' )

DROP TRIGGER [Deny_QueryWindowLogin_Trigger] ON ALL SERVER
 GO

Create TRIGGER Deny_QueryWindowLogin_Trigger ON ALL SERVER
WITH EXECUTE AS 'sa'
FOR LOGON AS
BEGIN
   DECLARE @data XML
   SET @data = EVENTDATA()
  DECLARE @AppName SYSNAME, @LoginName SYSNAME

  SELECT @AppName = [program_name] FROM sys.dm_exec_sessions WHERE session_id = @data.value('(/EVENT_INSTANCE/SPID)[1]', 'int')

SELECT @LoginName = @data.value('(/EVENT_INSTANCE/LoginName)[1]', 'sysname') IF @AppName= 'Microsoft SQL Server Management Studio - Query' AND @LoginName = 'DBA_ErrorLogUser'

BEGIN
             ROLLBACK ; --Disconnect the session
END
 END ;