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Discover Ludwig"at much" is not correct in written English.
It is not an established expression. If you want to use the phrase "at much," you should rephrase it to be more grammatically correct. For example, you could say "by a great deal," or "by a large amount."
Exact(60)
Public workers are also FIRED AT MUCH LOWER RATES.
He loses me here at "much as".
Publishing companies trade at much lower levels.
At much lower prices.
And at much greater cost.
I'm not good at much else".
Liquid liquid systems have folds at much lower contact angles.
but FeB became much more pronounced at much longer durations.
News and talk, however, transmit at much lower bit rates.
Exports are flowing again but at much reduced rates.
(Waste hauling is taxed at much higher rates than recyclables).
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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