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The phrase "illuminate the problem" is correct and can be used in written English.
It means to shed light on or make clear the details or aspects of a problem. Example: The information provided by the witness helped to illuminate the problem and allowed the detectives to finally solve the case.
Exact(7)
They illuminate the problem.
Another Mark Twain quote will illuminate the problem.
At times the music, like the lyrics, does illuminate the problem of a band taking itself too seriously.
And because everything that happens is intended to illuminate the problem that is Ms. Aladag's main concern — the so-called honor killings of women in Muslim communities in Europe and the Middle East — the behavior of the characters seems constricted.
The numbers illuminate the problem.
It does not illuminate the problem or reach toward common ground.
Similar(53)
The two episodes illuminate the problems the United States still faces in understanding the intentions of Al Qaeda and its affiliates.
Through investigating how players, as learners, structure their cognitive development, construct and negotiate their identity and sense of self, and make meaning while navigating a fundamentally "problem-based" context, we aim to illuminate the problem-solving processes emerging in such technology-facilitated environments.
A moral panic acts like a giant spotlight, illuminating the problem.
In a set of exceptionally interesting opinions, expressing diverse views, they illuminated the problem of money in politics.
The clever-but-tragic hash tags, not to mention the truly bizarre use of the word "famous," illuminates the problem much better than anything else in Weinergate.
More suggestions(18)
enlighten the problem
illuminate the issue
demonstrate the problem
explain the problem
clarify the problem
delineate the problem
illuminate the predicament
inform the problem
illuminate the subject
articulate the problem
illuminate the dilemma
illuminate the challenges
illuminate the troubles
stoking the problem
light the problem
turning the problem
clarifying the problem
highlight the problem
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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