Different logo on specific page / node
If you know the node NID of this special page, it would be a quick...

&lt;?php if ($_GET['q']=='node/NID'): ?&gt;
  &lt;div&gt;extra logo&lt;/div&gt;
&lt;?php endif; ?&gt;


...in your page.tpl.php file.  You could also create a special template for this node:

page--NID.tpl.php // for Drupal 7
page-NID.tpl.php  // for Drupal 6


...and have it in there all the time.

If you want to make sure that www.example.com/special uses a special template regardless of what node/NID it is really, eg, special is really an alias for node/6 or something, then you will need to get a bit more "special" with some preprocessing to look at the path alias and check if it is special and then do things different.  And I say preprocessing because there should be as little logic in the templates as possible.