Separate tables for logging?

I would like to log new products, updates to products and deletions of products (and the same for other schemata [customers, locations etc]). Would it be best to have a separate table (e.g. ProductLog, CustomerLog) for this, so that I can have a product foreign key as a field in the ProductLog, customer foreign key in the Customer Log etc? Or should I use one table to avoid creating essentially double the amount of tables?