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Discover Ludwig"found out by" is a perfectly correct and usable phrase in written English.
You could use it when someone discovers or learns something by means of their own observation or research (for example, by looking into something, asking questions, or doing an experiment). For example: "The truth about the missing money was found out by the police detectives after a long and tedious investigation."
Exact(60)
He found out by reading a magazine.
I found out by reading about it in The Villager".
I am sure that he has found out by now".
The team found out by analyzing tiny paint samples.
I found out by telephoning ten-year-old Lee Rostow Freedman.
As all of us found out by the end of the fight, some really yucky stuff.
I try to write about things that readers couldn't or wouldn't have found out by themselves.
In some of these cases, we found out by pure chance," he said.
She tells of having taken secret music lessons, which if found out by the Taliban might have gotten her killed.
Latte was almost found out by a National Socialist Party member and anti-Semite in the troupe.
Maybe he's found out by now dat he'll neveh live long enough to know duh whole of Brooklyn.
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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