You could check the current category and apply a different class with each logo,
$cur_topic = $queried_object->slug;
$my_class="default-logo";
switch ($cur_topic) {
case "food":
$my_class="food-logo";
break;
case "lifestyle":
$my_class="lifestyle-logo";
break;
case "fiction":
$my_class="fiction-logo";
break;
default:
$my_class="default-logo";
}
echo '<div class="' . $my_class . '"></div>';
Alternatively, check out the following plugin: