Here is a simple Log singleton in C#.

Updated: 7/25/2016

using System;
using System.IO;

namespace Rhyous.Logging
{
    public class Log
    {

        #region Singleton

        private static readonly Lazy<Log> Lazy = new Lazy<Log>(() => new Log());

        public static Log Instance { get { return Lazy.Value; } }

        internal Log()
        {
            LogFileName = "Example";
            LogFileExtension = ".log";
        }

        #endregion

        public StreamWriter Writer { get; set; }

        public string LogPath
        {
            get { return _LogPath ?? (_LogPath = AppDomain.CurrentDomain.BaseDirectory); }
            set { _LogPath = value; }
        } private string _LogPath;

        public string LogFileName { get; set; }

        public string LogFileExtension { get; set; }

        public string LogFile { get { return LogFileName + LogFileExtension; } }

        public string LogFullPath { get { return Path.Combine(LogPath, LogFile); } }

        public bool LogExists { get { return File.Exists(LogFullPath); } }

        public void WriteLineToLog(string inLogMessage)
        {
            WriteToLog(inLogMessage + Environment.NewLine);
        }

        public void WriteToLog(string inLogMessage)
        {
            if (!Directory.Exists(LogPath))
            {
                Directory.CreateDirectory(LogPath);
            }
            if (Writer == null)
            {
                Writer = new StreamWriter(LogFullPath, true);
            }

            Writer.Write(inLogMessage);
            Writer.Flush();
        }

        public static void WriteLine(string inLogMessage)
        {
            Instance.WriteLineToLog(inLogMessage);
        }

        public static void Write(string inLogMessage)
        {
            Instance.WriteToLog(inLogMessage);
        }
    }
}

Note: This is not tested with multiple threads as this is a simple example.