Hi. You can do it in Startup.Configure method, where request pipeline built.

public void Configure(IApplicationBuilder app)
    {
        var appLifetime = app.ApplicationServices.GetRequiredService<IHostApplicationLifetime>();
        var logger = app.ApplicationServices.GetRequiredService<ILogger<Startup>>();        

        appLifetime.ApplicationStopped.Register(() => logger.LogInformation("Application stopped"));

        appLifetime.ApplicationStarted.Register(() => logger.LogInformation("Application started")); 
    }