How can I make the "if" statement for a link to work fine if I want to show it only if it's not the "Index" page

In my application,the first page is Index.tml and I have a login form. The layout for this application has a menu with some links in it and I added another one which is called "Delogheza-te"=Log-out. What I want is that ,the "log-out link" to be visible only after the user logged-in. The log-out link should be visible on all pages except "Index.tml". How can I do that? I tryed this but it's wrong.

<t:if  t:page!="Index">
 <a href="#" t:type="PageLink" t:page="Index">Delogheaza-te</a>
 </t:if>