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The phrase "applying the same logic" is correct and usable in written English.
You can use it when you want to indicate that you are using a similar reasoning or rationale in a different context or situation.
Example: "If we consider the previous case, applying the same logic, we can conclude that this approach will also yield positive results."
Alternatives: "using the same reasoning" or "employing the same rationale".
Exact(22)
"And now we're applying the same logic and ethics to the global pandemic.
When Browne talks about the fears still keeping businesspeople in the closet, he is a powerful advocate, applying the same logic he once used on mergers and markets.
But let's hope he never gets round to applying the same logic to physicists' ability to evaluate dodgy papers on the arxiv.
Applying the same logic across all Australian states (with total combined annual expenditure on food of $158bn, compared with $48bn in Illinois) would mean that the same 20% shift to local food in Australia would lead to at least $50bn billion of new economic activity.
But applying the same logic to Japan, where growth has averaged only 0.7% a year over the past seven years, compared with a previous trend rate of 3-4%, one could argue that Japan's output has already fallen by as much as 15-20% relative to its previous trend.
Building a successful personal brand requires conformity in applying the same logic, accuracy and fairness pattern to identify you.
Similar(38)
Now apply the same logic to the Supreme Court.
You just apply the same logic to many different things.
It should apply the same logic to restrictions on sperm and egg donation.
If you apply the same logic to third-grade reading funding the same gaping differences result.
Many Europeans apply the same logic to free speech and Islamists.
More suggestions(16)
apply the same logic
applying the same coefficient
applying the same target
applying the same scaling
applying the same pressure
applying the same pilot
applying the same strategy
applying the same scheme
applying the same technique
applying the same resourcefulness
applying the same diligence
applying the same system
applying the same approach
applying the same kind
applying the same seed
applying the same methodology
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com