assume this class:

public class Logger
{
    static TextWriter fs = null;

    public Logger(string path)
    {
        fs = File.CreateText(path);
    }

    public static void Log(Exception ex)
    {
        ///do logging
    }

    public static void Log(string text)
    {
        ///do logging
    }
}

and I have to use this like:

Logger log = new Logger(path);

and then use Logger.Log() to log what I want.
the question is: is this a good design? to instantiate a class and then always call it's static method? any suggestion yield in better design is appreciated.