How to use Application.logMessageReceived for logging ?

You have to wrap the code from the link into a component and attach it to the scene:

     public class ExternalLoggerComponent : MonoBehaviour
     {
       public void Awake()
       {
         Debug.Log("ExternalLoggerComponent -> Awake");
       }
         
       public void OnEnable()
       {
         Debug.Log("ExternalLoggerComponent -> OnEnable");
         
         Application.logMessageReceivedThreaded += HandleLog;
       }
         
       public void OnDisable()
       {
         Debug.Log("ExternalLoggerComponent -> OnDisable");
         
         Application.logMessageReceivedThreaded -= HandleLog;
       }
         
       public void HandleLog(string logString, string stackTrace, LogType type)
       {
         // do some stuff
       }
     }
 

wo have a sctipt for the logMessageReceived .Just set the script into your MainCamera. I found it in a blog(http://www.cnblogs.com/tianyajuanke/p/4867249.html)

 using UnityEngine;
 using System.Collections;
 using System.Collections.Generic;
 using System.IO;
 using System.Text;
 
 public class LogHandler : MonoBehaviour 
 {
     //是否打开日志所在文件夹，默认不打开
     public bool openLogDir = false;
     //最多显示多少条日志到屏幕
     public int showLogSize = 3;
     //设置过滤显示到屏幕的关键字，多个关键字用 | 隔开
     public string filterString = "";
     //日志存储路径
     private string logSavePath;
     //存储显示到屏幕上的日志
     private List<string> logList;
     void Start () {
         logList = new List<string>();
         logSavePath = Application.persistentDataPath + "/log";
         if(openLogDir)
         {
             Application.OpenURL (Application.persistentDataPath);
         }
         //将本次日志与上次启动时的日志分离开
         using(StreamWriter writer = new StreamWriter(logSavePath, true, Encoding.UTF8))
         {
             writer.WriteLine("\n\n----------------------------- 日志分隔线 -----------------------------");
             writer.WriteLine("----------------------------- "+ System.DateTime.Now +" -----------------------------");
         }
         //注册日志处理函数
         Application.logMessageReceived += HandleLog;
     }
     
     void HandleLog(string logString, string stackTrace, LogType type)
     {
         //将所有日志写入到日志文件
         using(StreamWriter writer = new StreamWriter(logSavePath, true, Encoding.UTF8))
         {
             writer.WriteLine(logString + "\n\t\t" + type + ": " + stackTrace.Replace("\n","\n\t\t"));
         }
         //设置过滤条件，将指定类型、包含某些字符串的日志保存到屏幕日志窗器中
         bool show = false;
         //置过滤条件:指定类型
         if (type == LogType.Error || type == LogType.Exception || type == LogType.Warning)
         {
             show = true;
         }
         //置过滤条件:包含指定关键字，多个关键字用 | 隔开
         foreach (string str in filterString.Split('|'))
         {
             if(logString.Contains(str))
             {
                 show = true;
                 break;
             }
         }
         if(show)
         {
             logList.Add (logString);
             if (logList.Count > showLogSize) 
             {
                 logList.RemoveAt(0);
             }
         }
     }
 
     void OnGUI()
     {
         GUI.color = Color.red;
         for (int i = 0; i < logList.Count; ++i)
         {
             GUILayout.Label(logList[i]);
         }
     }
 }

You can learn it for yourself.