I have used a Java bean for setting and getting userName/id,password and its login process.
Look at here :

<h:inputText id="userName" value="#{UserBean.userName}"></h:inputText>

The above code creates an instance of UserBean and sets the property userName to the entered value.

Note:

<h:commandButton value="Login" action="#{UserBean.login}" type="submit"></h:commandButton>

This calls the login() in UserBean which updates the database about login status directly using DAO's.

But Now i need to have a log out(which is a hyperlink) redirecting to a logout servlet.
//com.servlet.logout.java
protected void doGet(HttpServletRequest request, HttpServletResponse response) throws ServletException, IOException {
HttpSession session = request.getSession();
session.invalidate();
response.sendRedirect(request.getContextPath()+"/loginForm.faces");
}

How do i get now update the database using the DAO thats available for updation that I did using the bean(previously did for login)?.

Two issues that i face now:
1) If I use servlet to invalidate request, how do I then use logout method in DAO?
2) As I have to call the DAO's updateLog(String userName,String logStatus) from where could I get userName from?