Meaning:

Do something in the same way as someone else does to be like him/her or successful as he/she is.

If you take a leaf out of someone's book, you behave like him/her because you will gain advantages from it.

Example:

Maybe I should take a leaf out of Jenny's book and start exercising.
(She's always in good shape because she exercises every day.)

I will take a leaf out of his book. It's clear to see how he learned to become a fluent English speaker.

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