I think one of the simplest way to achieve ( and perhaps not the better ) is to create a class ‘btn-hidden’ or similar, with display:none in the definition. Then, when you are in your template, control if user is logged in or not ( function is_user_logged_in() ) and if user is in one or other page ( depending on your configuration, this can be done in different ways, it could be by is_page(‘Page Name’) function perhaps ). Finally, depending on the combination of these elements, apply the class to the buttons that should be hidden.
Hope this helps, but I think the question needs some more information about the context.