To control this with cookies:
<cfif Not IsDefined('cookie.yoursite')>
Show login image
<cfelseif IsDefined('cookie.yoursite')>
Show LogOut image
</cfif>
Once user has logged in using your login form, set the
cookie:
<cfcookie name="yoursite" value=#id#>
et voila?! (if storing the user's ID in a cookie I would
recommend encypting first, using #Encrypt())