Write a message to a log I have started to read Robert C. Martin Clean Code book.

To learn and gain more expreiences I wrote a single Log class. So I want some suggestions to improve this code..
This is a part of the Log class:

public class FileLogger : ILog
{
    private string directoryPath = string.Empty;
    private string fileName = string.Empty;

    public FileLogger(string logDirectoryPath, string logFileName)
    {
        if (string.IsNullOrEmpty(logDirectoryPath))
        {
            throw new ArgumentException(nameof(logDirectoryPath), "Write some error message...");
        }

        if (string.IsNullOrEmpty(logFileName))
        {
            throw new ArgumentException(nameof(logFileName), "Write some error message...");
        }

        this.directoryPath = logDirectoryPath;
        this.fileName = logFileName;
    }

    public void LogMessage(string message)
    {
        try
        {
            if (!string.IsNullOrEmpty(message))
            {
                if (!LogDirectoryExists(directoryPath))
                {
                    CreateLogDirectory(directoryPath);
                }

                WriteToLogFile(message);
            }
        }
        catch (Exception ex)
        {
            //Catch exception, do something...
        }
    }

    private bool LogDirectoryExists(string logDirectoryPath)
    {
        return Directory.Exists(logDirectoryPath);
    }

    private void CreateLogDirectory(string logDirectoryPath)
    {
        Directory.CreateDirectory(logDirectoryPath);
    }

    private void WriteToLogFile(string message)
    {
        using (var logFile = new FileStream(Path.Combine(directoryPath,fileName), FileMode.Append, FileAccess.Write))
        {
            using (var logFileWriter = new StreamWriter(logFile))
            {
                logFileWriter.Write(message);
            }
        }
    }
}


I wrote 3 different function to write a message to a log. I try to use SRP and Command Query Separation, but I don't sure this is a good in this way. Maybe there are another problems with this code, example naming or variable declarations.
After discussion in comments your code became much better.

Also if directoryPath and fileName will not be changed after initialization in constructor you can define these fields as readonly:

private readonly string directoryPath = string.Empty;
private readonly string fileName = string.Empty;


This code


using (var logFile = new FileStream(Path.Combine(directoryPath,fileName), FileMode.Append, FileAccess.Write))
{
    using (var logFileWriter = new StreamWriter(logFile))
    {
        logFileWriter.Write(message);
    }
}



can be replaced with

File.AppendAllText(Path.Combine(directoryPath, fileName), message);


Also ArgumentException's constructor takes message as first argument and paramName as second, so you need to call it like this:

throw new ArgumentException("Write some error message...", nameof(logDirectoryPath));