When using RedisSessionStateProvider and/or RedisOutputCacheProvider, and want to specify loggingClassName and loggingMethodName to write to log4Net.

Log4NetTextWriter.cs

using System;
using System.IO;
using System.Text;
using log4net;

namespace RedisUtil
{
	public class Log4NetTextWriter : TextWriter
	{
		private static readonly ILog Log = LogManager.GetLogger(typeof(Log4NetTextWriter));

		public override Encoding Encoding => Encoding.UTF8;

		#region properties

		private StringBuilder Buffer { get; }

		private string LogPrefix { get; }

		#endregion properties ;

		public override void Flush()
		{
			if (Buffer != null && Buffer.Length > 0)
			{
				WriteLine();
			}
		}

		protected override void Dispose(bool disposing)
		{
			Flush();
			base.Dispose(disposing);
		}

		#region public constructors

		public Log4NetTextWriter(string logPrefix = null) : this(null, logPrefix)
		{

		}

		public Log4NetTextWriter(IFormatProvider formatProvider, string logPrefix) : base(formatProvider)
		{
			Buffer = new StringBuilder();
			LogPrefix = logPrefix;
		}

		#endregion public constructors

		#region public Write() overloads
		public override void Write(bool value)
		{
			Buffer.Append(value);
		}
		public override void Write(char value)
		{
			Buffer.Append(value);
		}
		public override void Write(char[] buffer)
		{
			Buffer.Append(buffer);
		}
		public override void Write(char[] buffer, int index, int count)
		{
			Buffer.Append(buffer, index, count);
		}
		public override void Write(decimal value)
		{
			Buffer.Append(value);
		}
		public override void Write(double value)
		{
			Buffer.Append(value);
		}
		public override void Write(float value)
		{
			Buffer.Append(value);
		}
		public override void Write(int value)
		{
			Buffer.Append(value);
		}
		public override void Write(long value)
		{
			Buffer.Append(value);
		}
		public override void Write(object value)
		{
			Buffer.Append(value);
		}
		public override void Write(string format, object arg0)
		{
			Buffer.AppendFormat(FormatProvider, format, arg0);
		}
		public override void Write(string format, object arg0, object arg1)
		{
			Buffer.AppendFormat(FormatProvider, format, arg0, arg1);
		}
		public override void Write(string format, object arg0, object arg1, object arg2)
		{
			Buffer.AppendFormat(FormatProvider, format, arg0, arg1, arg2);
		}
		public override void Write(string format, params object[] arg)
		{
			Buffer.AppendFormat(FormatProvider, format, arg);
		}
		public override void Write(string value)
		{
			Buffer.Append(value);
		}
		public override void Write(uint value)
		{
			Buffer.Append(value);
		}
		public override void Write(ulong value)
		{
			Buffer.Append(value);
		}
		#endregion public Write() overloads

		#region public WriteLine() overloads
		public override void WriteLine()
		{
			string logMessage = Buffer.ToString();

			Buffer.Length = 0;
			var tempLogPrefix = string.IsNullOrEmpty(LogPrefix) ? "" : $"{LogPrefix}() --> ";
			Log.Info($"{tempLogPrefix}{logMessage}");
		}
		public override void WriteLine(bool value)
		{
			Write(value);
			WriteLine();
		}
		public override void WriteLine(char value)
		{
			Write(value);
			WriteLine();
		}
		public override void WriteLine(char[] buffer)
		{
			Write(buffer);
			WriteLine();
		}
		public override void WriteLine(char[] buffer, int index, int count)
		{
			Write(buffer, index, count);
			WriteLine();
		}
		public override void WriteLine(decimal value)
		{
			Write(value);
			WriteLine();
		}
		public override void WriteLine(double value)
		{
			Write(value);
			WriteLine();
		}
		public override void WriteLine(float value)
		{
			Write(value);
			WriteLine();
		}
		public override void WriteLine(int value)
		{
			Write(value);
			WriteLine();
		}
		public override void WriteLine(long value)
		{
			Write(value);
			WriteLine();
		}
		public override void WriteLine(object value)
		{
			Write(value);
			WriteLine();
		}
		public override void WriteLine(string format, object arg0)
		{
			Write(format, arg0);
			WriteLine();
		}
		public override void WriteLine(string format, object arg0, object arg1)
		{
			Write(format, arg0, arg1);
			WriteLine();
		}
		public override void WriteLine(string format, object arg0, object arg1, object arg2)
		{
			Write(format, arg0, arg1, arg2);
			WriteLine();
		}
		public override void WriteLine(string format, params object[] arg)
		{
			Write(format, arg);
			WriteLine();
		}
		public override void WriteLine(string value)
		{
			Write(value);
			WriteLine();
		}
		public override void WriteLine(uint value)
		{
			Write(value);
			WriteLine();
		}
		public override void WriteLine(ulong value)
		{
			Write(value);
			WriteLine();
		}

		#endregion public WriteLine() overloads

	}
}

RedisLogger.cs

using System.IO;

namespace RedisUtil
{
	public class RedisLogger
	{
		public static TextWriter LogSessionStateActivity()
		{
			return new Log4NetTextWriter("REDIS-SESSION-STATE");
		}
		public static TextWriter LogOutputCacheActivity()
		{
			return new Log4NetTextWriter("REDIS-OUTPUT-CACHE");
		}
	}
}

web.transform.config

<system.web>
  <sessionState mode="Custom" customProvider="MySessionStateStore">
    <providers>
		  <add name="MySessionStateStore" 
        type="Microsoft.Web.Redis.RedisSessionStateProvider" 
        databaseId="0" 
        applicationName="REDIS-SESSION" 
        retryTimeoutInMilliseconds="10000" 
        connectionTimeoutInMilliseconds="10000" 
        operationTimeoutInMilliseconds="2000" 
        connectionString="{name}.redis.cache.windows.net:6380,password={accessKey},ssl=True,abortConnect=False" 
        loggingClassName="RedisUtil.RedisLogger" 
        loggingMethodName="LogSessionStateActivity" />
    </providers>
  </sessionState>
  <caching>
    <outputCache defaultProvider="MyRedisOutputCache">
      <providers>
        <add name="MyRedisOutputCache" 
            type="Microsoft.Web.Redis.RedisOutputCacheProvider" 
            databaseId="1" 
            applicationName="REDIS-CACHE" 
            connectionString="{name}.redis.cache.windows.net:6380,password={accessKey},ssl=True,abortConnect=False" 
            loggingClassName="RedisUtil.RedisLogger" 
            loggingMethodName="LogOutputCacheActivity" />
      </providers>
    </outputCache>
  </caching>  
</system.web>