socket programming multiple client to one server

How do you handle multiple client to connect to one server? I have this LogServer.java

import javax.net.ssl.*;
import javax.net.*;
import java.io.*;
import java.net.*;

public class LogServer {
  private static final int PORT_NUM = 5000;
  public static void main(String args[]) {
    ServerSocketFactory serverSocketFactory =
      ServerSocketFactory.getDefault();
    ServerSocket serverSocket = null;
    try {
      serverSocket =
        serverSocketFactory.createServerSocket(PORT_NUM);
    } catch (IOException ignored) {
      System.err.println("Unable to create server");
      System.exit(-1);
    }
    System.out.printf("LogServer running on port: %s%n", PORT_NUM);
    while (true) {
      Socket socket = null;
      try {
        socket = serverSocket.accept();
        InputStream is = socket.getInputStream();
        BufferedReader br = new BufferedReader(
          new InputStreamReader(is, "US-ASCII"));
        String line = null;
        while ((line = br.readLine()) != null) {
          System.out.println(line);
        }
      } catch (IOException exception) {
        // Just handle next request.
      } finally {
        if (socket != null) {
          try {
            socket.close();
          } catch (IOException ignored) {
          }
        }
      }
    }
  }
}

and an embedded applet with part of the code like this e.g

import java.io.*;
import java.util.logging.*;

public class LogTest
{
  private static Logger logger = Logger.getAnonymousLogger();

  public static void main(String argv[]) throws IOException
  {
    Handler handler = new SocketHandler("localhost", 5000);
    logger.addHandler(handler);
    logger.log(Level.SEVERE, "Hello, World");
    logger.log(Level.SEVERE, "Welcome Home");
    logger.log(Level.SEVERE, "Hello, World");
    logger.log(Level.SEVERE, "Welcome Home");
  }
}

now the question is if I run "java LogServer" on the server, it will open the applicatio