Startup.cs

public class Startup
{
    ...
    public void ConfigureServices(IServiceCollection services)
    {
        ...
        services.AddElmahIo(o =>
        {
            o.ApiKey = "{API_KEY}";
            o.LogId = new Guid("{LOG_ID}");
        });
        ...
    } 
    ...
    public void Configure(IApplicationBuilder app, IHostingEnvironment env)
    {
        app.UseElmahIo();
    }
}