C# lock statement block: In a multithreading scenario how bad will be the performance hit?

Hi,
I have an existing code which apart from doing its main job writes to a log file. Now, the application is multithreaded and multiple threads can try to write to the log file. The existing code does not take care of thread synchronization. The basic structure of the code is -

public class A
{
     public void writeFullLogFile()
     {
          //call the function that actually writes to the log file
          B.writeToFile();
     }
}

public class B
{
     public static void writeToFile()
     {
          //actual file write happens here.
     }
}

All I am planning to do get the synchronization is to put a lock statement like below:

public class A
{
     private static Object lockMe = new Object();
     public void writeFullLogFile()
     {
          //call the function that actually writes to the log file
          lock(lockMe)
          {
               B.writeToFile();
          }
     }
}


Now, I want to know how badly does the lock statement affects the performance? How does the performance degrade with an increase in the number of concurrent threads?

Without changing my existing solution much is there a better way to have synchronization?