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DSkoog
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#Maple, 32 30 bytes

f:=x->`if`(x>1,1+f(log(x)),0); 

Test cases:

> f(0.); 0 > f(1.); 0 > f(2.); 1 > f(3.); 2 > f(4.); 2 > f(3814279.); 3 > f(3814280.); 4 
DSkoog
  • 580
  • 3
  • 9