Here are the changes that you need to make in your ASP.Net Core web application to configure Serilog logging with SQL server sink.

a. Install the following libraries from Nuget, using the Nuget Package Manager
Serilog.AspNetCore
Serilog.Extensions.Logging
Serilog.Settings.AppSettings
Serilog.Settings.Configuration
Serilog.Sinks.MSSqlServer

b. Program.cs:

using Microsoft.AspNetCore;
using Microsoft.AspNetCore.Builder;
using Microsoft.AspNetCore.Hosting;
using Microsoft.Extensions.Configuration;
using Serilog;
using System;
using System.IO;

namespace Scrubber
{
  public class Program
  {
    public static void Main(string[] args)
    {
      var path = Directory.GetCurrentDirectory();
      var environmentName =Environment.GetEnvironmentVariable("ASPNETCORE_ENVIRONMENT") ?? "Production";

      var configuration = new ConfigurationBuilder()
      .SetBasePath(path)
      .AddJsonFile("appsettings.json", optional: false, reloadOnChange: true)
      .AddJsonFile($"appsettings.{environmentName}.json", optional: false, reloadOnChange: true)
      .Build();

      Log.Logger = new LoggerConfiguration()
        .Enrich.FromLogContext()
        .ReadFrom.Configuration(configuration)
        .CreateLogger();

      try
      {
        WebHost.CreateDefaultBuilder(args)
          .UseStartup()
          .UseSerilog()
          .Build()
          .Run();
      }
      finally
      {
        Log.CloseAndFlush();
      }
    }
  }
}

AppSettings.json:

{
  "Serilog": {
    "Using": [ "Serilog.Sinks.MSSqlServer" ],
    "MinimumLevel": "Information",
    "WriteTo": [
      {
        "Name": "MSSqlServer",
        "Args": {
          "connectionString": "YourSQLServerConnectionString",
          "tableName": "Logs",
          "autoCreateSqlTable": true
        }
      }
    ]
  }
}