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The phrase "an extent to which" is correct and usable in written English.
It can be used to discuss the degree or level of something in relation to a specific factor or condition.
Example: "The study aims to measure the extent to which environmental factors influence mental health."
Alternatives: "the degree to which" or "the level to which".
Exact(18)
On the other hand, there's definitely an extent to which the hashtag is in bad taste.
"There's only an extent to which that will ever be successful".
There's also probably an extent to which the spying there is overstated.
Isn't there an extent to which torture creates plots, leads to recruitment of enemies of the United States?
But there is an extent to which a company can, with an ad, invite a little bit of national reflection.
Such is the current turmoil at Blackpool Football Club, there is an extent to which whatever happens on the field is almost peripheral.
Similar(42)
Kristol basically believes that Ohio and Pennsylvania aren't reliable firewalls for Clinton, and there's a extent to which he could be right - after all, that "lay back and wait in you firewall states" strategy didn't work for Giuliani.
The affective aspect (A): The extent to which the respondent feels the medical professional (MP) listens, understands and is interested.
Centrality is a measure of the extent to which a nest occupies an important position in the network (Newman 2003b).
Again, though generally considered to be a Thomist, the extent to which he was is a matter of some debate.
Phi is a measure of the extent to which a given system — for example, a brain circuit — is capable of fusing these distinctive bits of information.
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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