C# .Net - How to make application wait until all threads created in Library are finished

I am trying to create a logging library and things are good until the application shutdown is called. When application shutdown is called, any unfinished thread is killed and the specific log is lost.

As of now application exits even before the first 10 threads are complete. I want help on how to make the application wait until all threads created by library are done.

NOTE: Requirement I got are like this. Modifications should be only in the class 'Logging' since this will be a library and will be provided to end users. Handling of logging issues during app shutdown must be done within it. This is where I have trouble now.

Alternatively a solution like create an event in logging class to trigger all logging complete, and ask user to call app exit on that event is possible, but that I am trying to avoid since it adds that burden to end user and adds complexity for implementations. There is a possibility they may skip it, which I do not want. I am looking for a solution like user should do 'Logging.AddException(....)' and then forget about it.

Please help. Provide comments if you are not clear about the idea.

Here is the full code abstract which you can put into a console application. Note: Look for comments in CASE 1 and CASE 2.

using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.Linq;
using System.Text;
using System.Threading;
using System.Threading.Tasks;

namespace MultithreadKeepAlive
{
class Program
{
    static void Main(string[] args)
    {
        LogLoadTest();
        Logging.AddExceptionEntryAsync(new Exception("Last Exception"));

        /*
         * USE CASE 1: Enable the below lines and you will see how long it is supposed to take.
         * Notice that currentDomain_ProcessExit will not trigger if below gets uncommented
         */
        //Console.WriteLine("Main thread wait override");
        //Console.ReadLine();
    }

    static void LogLoadTest()
    {
        //In real world this will be called from any place of application like startup or just after application shutdown is initiated.
        //: NOTICE: Unlike the sample here, this will never be on loop and I am not looking for handling multithreads in this class.
        //      That responsibility I am planning to assign to Logging class.
        // AND ALSO the class Logging is going to be in a seperate signed assembly where user of this class ('Program') should not worry about multithreads.
        Task t;
        for (int i = 0; i < 40; i++)
        {
           t =  Logging.AddExceptionEntryAsync(new Exception("Hello Exception " + i), "Header info" + i);
        }
    }
}

public class Logging
{
    static List<Task> tasks = new List<Task>();

    static AppDomain currentDomain;
    static Logging()
    {
        currentDomain = AppDomain.CurrentDomain;
        currentDomain.ProcessExit += currentDomain_ProcessExit;
    }

    public static async Task AddExceptionEntryAsync(Exception ex, string header = "")
    {
        Task t = Task.Factory.StartNew(() => AddExceptionEntry(ex, header));
        tasks.Add(t);
        await t;
    }

    public static void AddExceptionEntry(Exception ex, string header)
    {
        /* Exception processing and write to file or DB. This might endup in file locks or 
         * network or any other cases where it will take delays from 1 sec to 5 minutes. */
        Thread.Sleep(new Random().Next(1, 1000));
        Console.WriteLine(ex.Message);
    }

    static void currentDomain_ProcessExit(object sender, EventArgs e)
    {
            Console.WriteLine("Application shutdown triggerd just now.");
            Process.GetCurrentProcess().WaitForExit();    //1st attempt.
            //Task.WaitAll(tasks.ToArray()); //2nd attempt
            while (tasks.Any(t => !t.IsCompleted)) //3rd attempt.
            {
            }
            /* USE CASE 2: IF WORKING GOOD, THIS WILL BE DISPLAYED IN CONSOLE AS LAST 
             * MESSAGE OF APPLICATION AND WILL WAIT FOR USER. THIS IS NOT WORKING NOW.*/
            Console.WriteLine("All complete"); //this message should show up if this work properly
            Console.ReadLine(); //for testing purpose wait for input from user after every thread is complete. Check all 40 threads are in console.
    }
}

}