"by the example" is correct and usable in written English.
For example, you could say, "Students should learn by the example set by their peers."
Led by the example of Sinatra, most of these artists enjoyed some degree of success.
We who survive are challenged and improved by the example he set for us.
"At the time, I was influenced by the example of my father.
Maureen, buoyed by the example of her Prime Minister, begins to assert herself in curious ways.
He is inspired, and challenged, by the example of Merle Haggard.
"She could tell Scientology worked by the example I set," Haggis told the magazine.
Mr. Smith said he was inspired by the example set by Mr. Richt.
But, frightened by the example of Eastern Europe, they fear any accompanying decentralization of political power.
It's a solution suggested to me by the example of Thomas Pynchon.
All her life, she says, she has been inspired by the example of her father.
Inspired by the example of Smith, Robert Capa and other photojournalists, Mr. Greene discovered his vocation.
