Help Please!!!

2²⁰⁰ < n¹⁰⁰ < (130n)⁵⁰

 

Take the 50^th root:     2⁴ < n² < 130n     --->     16 < n² < 130n

 

For  16 < n²  to be true, n >= 5

For  n² < 130n  to be true, n<= 129

 

So, I think that it will be true for all positive integers in the set:  { 5, 6, 7, ..., 128, 129 }