Thaumatology: Sorcery says, on p.5:
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The full cost of the spell cannot exceed the cost of the caster’s Sorcerous Empowerment.
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That's its full cost with all modifiers applied. The term "base cost" only shows up in that PDF on p.11, when you're dealing with enhancing an attack using Imbuements. And there it's quite clear that the full cost after modifiers is what matters.
If you can tell us where you ran into the "base cost" idea, we can probably sort it out.