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The phrase "applied the methods" is correct and usable in written English.
You can use it when discussing the implementation or use of specific techniques or approaches in a particular context, such as research or problem-solving.
Example: "In her research, she applied the methods outlined in the previous chapter to gather data effectively."
Alternatives: "utilized the techniques" or "employed the strategies."
Exact(48)
The Adnotationes, not printed until 1505, applied the methods of humanist philology to a sacred text.
Later she applied the methods of cultural anthropology to the Hollywood motion-picture community, publishing the results as The Dream Factory (1950).
His successor at Alexandria, Origen, showed less interest in literary and aesthetic matters but was a greater scholar and thinker; he first applied the methods of Alexandrian philology to the text of the Bible.
Möbius's mathematical papers are chiefly geometric; in many of them he developed and applied the methods laid down in his Der barycentrische Calkul (1827; "The Calculus of Centres of Gravity").
May 26 , 1867Hoboken, New Jersey January 10 , 1937Chicago, Illinois Julius Stieglitz, (born May 26 , 1867 Hoboken, N.J., U.S. died Jan . 10 , 1937Chicago) U.S. chemist who interpreted the behaviour and structure of organic compounds in the light of valence theory and applied the methods of physical chemistry to organic chemistry.
We applied the methods of translation and back – translation and experts analyzed translations.
Similar(12)
William Faulkner applied the method to stories that might seem improbably melodramatic if told in a more traditional way.
The researchers applied the method to a database of actively managed domestic equity mutual funds from the beginning of 1975 through 2006.
We applied the method presented above to UK urban areas.
We applied the method of detecting nonrandomness to the publicly available PPI dataset for humans [29].
We next applied the method on a variety of TSE affected samples.
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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