If you need to have exactly the same content of the master excepted the logo of the website, a very simple solution is to replace the logo by a keyword that will be resolved when the website will be displayed.
Of course this depend the way that the logo is display.
Some Joomla template, may setup the logo via a CSS and in this case, it is more difficult to create variant depending on the website.
Some are using a module to display the logo. In this case, you may perhaps change the custom HTML module content to replace the hardcoded logo by a keyword.
Some are directly managed inside the Joomla template code that may have to be adjusted.
Once you have the keyword then the idea is to replace the keyword with the real logo path. This can be done for example with the free Search/Replace plugin that you can find on our free download section.
www.jms2win.com/en/component/docman/doc_...rch--replace-utility
With the Search/Replace plugin, you can have different S/R file depending on the website ID or domain and therefore create different path to the logo.
With the Search/Replace plugin, you can have a same website content except some parts that are identified by keywords and resolved when displaying the website.