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"used the same way" is correct and can be used in written English.
It is often used to compare how one thing is used in a similar manner as another thing. For example: - "The words 'affect' and 'effect' are often confused, but they are not used the same way." - "In this context, 'they' and 'them' can be used the same way." - "Both of these medications are used the same way - take one pill every morning."
Exact(32)
2. a string used the same way.
The department's 18-wheelers have been used the same way in other instances.
[Laughs] And there are people who are so tired of being used the same way again and again.
The Queens diving board could be used the same way, as the ultimate box seat, he said.
As far as means the same as but cannot be used the same way as as for.
The Peacekeeper and the BearCat are used the same way: to approach a threat and allow the officers inside to safely exit from rear doors.
Similar(28)
The normalized mean speed vnorm can be calculated using the same way.
now, use the same way as (1), we can obtain the result (2).
By using the same way as in Corollary 4.10, we can get Corollary 4.11.
Using the same way, we can define the other pair of sparse projectors.
And PTF-POS uses the same way as ours to combine phrase frequency and the first occurrence phrase position.
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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