Changing logo when signed in
In general, every .tpl.php has what is called a "preprocess" function.  The default one for page.tpl.php is template_preprocess_page().  This sets up the variables that are available in the template.  Other modules and themes can have their own; then don't replace each other, rather, they all run in a defined order.

So, you would add in a preprocess function for your theme's template.php like:

function MYTHEME_preprocess_page(&amp;$variables) {
  if (user_is_logged_in()) {
    $path = drupal_get_path('theme', 'MYTHEME');

    $variables['logo'] = file_create_url($path . '/images/inner_logo.png');
  }
}


This will check to see if the user is logged in using the proper API call (program to the interface not the implementation), and then change the logo variable to a new path from within your theme.  Just make sure you clear the Drupal caches from admin/config/development/performance first so the function gets picked up.