You're right to question the usage because 'take place' is more often used for organized events. In this instance it's better to use 'happen' or 'occur'.

Hi Mayi, The answer to your question is no. The use of "by" infers "on or before" age 35. The word "in" is not applicable. I hope this helps, Stephen

No if you are going to use in it can refer to future time, for example "Take place in 35 years" it alters the intended meaning. Also using in can refer to a setting. "Take place in China." The sentence would read better if typed; "80 percent of life's most defining moments take place by the age of 35."