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The phrase "at a far higher" is correct and usable in written English.
It can be used to compare levels, quantities, or degrees, indicating that something is significantly greater than another.
Example: "The new model operates at a far higher efficiency than its predecessor."
Alternatives: "at a significantly higher" or "at a much greater".
Exact(59)
In recent years inflation has risen at a far higher rate than average earnings.
In the world of car collecting, such exclusivity usually comes at a far higher price.
They won medals at a far higher rate than French soldiers.
But this week's listing at a far higher price caught city officials by surprise, Mr. LaBonge said.
The test was at a far higher altitude than the near Earth orbit of the failing satellite.
Having bought the item, the missing piece would be replaced and it would be resold at a far higher price.
There are gender disparities as well: black men marry outside the race at a far higher rate than black women.
Lehman's commercial-real-estate assets, in particular, were being carried on the firm's books at a far higher value than was realistic.
THE Arctic ice cap melted this summer at a shocking pace, disappearing at a far higher rate than predicted by even the most pessimistic experts in global warming.
Officials acknowledge that some are apt to become sicker or fall, ending up in nursing homes at a far higher cost.
Not only did these patients adhere to medications at a far higher rate than patients usually do — this adherence also translated to excellent blood pressure and cholesterol control.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com