Powers of 2 Go In, Powers of 2 Come Out

Algebra Level 3

Let ff be a function with the following properties:

  • f(1)=1f(1) = 1
  • f(2n)=nf(n)f(2n) = n \cdot f(n) for all positive integers nn

What is the value of f(2100)f(2^{100})?

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