Application.RegisterLogCallback  

var output : String = "";
var stack : String = "";

function OnEnable () {
    Application.RegisterLogCallback(HandleLog);
}

function OnDisable () {
    // Remove callback when object goes out of scope
    Application.RegisterLogCallback(null);
}

function HandleLog (logString : String, stackTrace : String, type : LogType) {
    output = logString;
    stack = stackTrace;
}

using UnityEngine;
using System.Collections;

public class example : MonoBehaviour {
    public string output = "";
    public string stack = "";
    void OnEnable() {
        Application.RegisterLogCallback(HandleLog);
    }
    void OnDisable() {
        Application.RegisterLogCallback(null);
    }
    void HandleLog(string logString, string stackTrace, LogType type) {
        output = logString;
        stack = stackTrace;
    }
}

import UnityEngine
import System.Collections

class example(MonoBehaviour):

    public output as string = 

    public stack as string = 

    def OnEnable():
        Application.RegisterLogCallback(HandleLog)

    def OnDisable():
        Application.RegisterLogCallback(null)

    def HandleLog(logString as string, stackTrace as string, type as LogType):
        output = logString
        stack = stackTrace