The wordpress logout way requires you to redirect to their logout page. Nice way is to use a custom url, in this case pointing to /logout, and code (no need to create page)

Using built in WordPress redirect_to functionality On a page you want to redirect back to after login If you’re placing the login form of your home page (or some other page to the default) Redirect wp-login.php On a page you want to redirect back to after login Catch for page with your login form