Not sure if that exact code will work, but doing a quick search on the forums turned up this thread: (you'd have to modify for the logo token. I've pasted the code from the thread below)
<% If DotNetNuke.Security.PortalSecurity.IsInRole("Registered Users") %>
<li><dnn:USER runat="server" id="dnnUSER" /></li>
<% Else %>
<li><dnn:LOGIN runat="server" id="dnnLOGIN" /></li>
<% End If %>
<% If DotNetNuke.Security.PortalSecurity.IsInRoles(PortalSettings.AdministratorRoleName) %>
<li><dnn:LOGIN runat="server" id="dnnLOGINAdmin" /></li>
<% End If %>
If you don't need the control over the layout then you can use this method from DNNcreative.