Logging Repro

Function1.cs

using System.IO;
using System.Threading.Tasks;
using Microsoft.AspNetCore.Http;
using Microsoft.AspNetCore.Mvc;
using Microsoft.Azure.WebJobs;
using Microsoft.Azure.WebJobs.Extensions.Http;
using Microsoft.Extensions.Logging;
using Newtonsoft.Json;

namespace MyNamespace
{
    public class Function1
    {
        private Service<MyOtherClass> _service;

        public Function1(Service<MyOtherClass> service)
        {
            _service = service;
        }

        [FunctionName("Function1")]
        public async Task<IActionResult> Run(
            [HttpTrigger(AuthorizationLevel.Function, "get", "post", Route = null)] HttpRequest req,
            ILogger log)
        {
            _service.Log();

            log.LogInformation("C# HTTP trigger function processed a request.");

            string name = req.Query["name"];

            string requestBody = await new StreamReader(req.Body).ReadToEndAsync();
            dynamic data = JsonConvert.DeserializeObject(requestBody);
            name = name ?? data?.name;

            return name != null
                ? (ActionResult)new OkObjectResult($"Hello, {name}")
                : new BadRequestObjectResult("Please pass a name on the query string or in the request body");
        }
    }
}

Startup.cs

using Microsoft.Azure.Functions.Extensions.DependencyInjection;
using Microsoft.Extensions.DependencyInjection;
using Microsoft.Extensions.Logging;
using MyNamespace;

[assembly: FunctionsStartup(typeof(Startup))]

namespace MyNamespace
{
    public class Startup : FunctionsStartup
    {
        public override void Configure(IFunctionsHostBuilder builder)
        {
            RegisterService<MyOtherClass>(builder);
        }

        private static void RegisterService<T>(IFunctionsHostBuilder builder)
        {
            builder.Services.AddLogging(options =>
            {
                options.AddFilter(typeof(T).FullName, LogLevel.Information);
            });

            builder.Services.AddSingleton<Service<T>>();
        }
    }

    public class MyOtherClass
    {
    }

    public class Service<T>
    {
        private ILogger<T> _logger;

        public Service(ILogger<T> logger)
        {
            _logger = logger;
        }

        public void Log()
        {
            _logger.LogTrace("Trace");
            _logger.LogInformation("Information");
            _logger.LogError("Error");
        }
    }
}