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The phrase "achieve a higher" is correct and usable in written English.
You can use it whenever you want to talk about improving or elevating something. For example, "My goal is to achieve a higher level of success."
Exact(60)
Their goal is to achieve a higher rate of full-priced sales.
The best known Sufi tradition is dervishes' dancing to achieve a higher state of awareness.
To achieve a higher rate of pregnancy, we reduced the injection volume to ∼2 pl.
Two, to achieve a higher rate of commercialization for Cornell research, including more startups.
In the past, students studied to achieve a higher economic and social standing than their peers.
Nowhere is this more obvious than in Japan, where secondary-school leavers achieve a higher literacy level than English graduates.
"Millennials are the first generation unlikely to achieve a higher standard of living than their parents enjoyed.
Over the weekend, Finance Minister Laurent Fabius of France emphasized the need to achieve a higher rate.
Fulham, after four home wins in a row, may start to believe they can achieve a higher standing.
Though not, it seems, if you achieve a higher level of education than them or if you are a woman.
Why does SCALE-UP achieve a higher rate of sustainability?
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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