Use order the following functions by growth rate, please give your justifications.

3n² + n + 4, 2¹⁰⁰⁰, 5n(logn)³, 2^logn, n^logn, (logn)ⁿ.

For example, we can compare 5n(logn)³ with n^logn as follows:

1. Apply the logarithm and exponential formulas to transform:
2. Apply the logarithm and exponential formulas to transform:

Plogn 2log(logo) 2lognulogn 2(logn)