Algorithm Question: Please explain me(with some examples) the best way to find out TILDE approximation for any quantities, especially with logarithm. I've some basic idea of TILDE approximation, like big thing eats small thing, but i'm struggling to find out TILDE approximation for log expressions, or critical expressions. Please see below some examples, but basically i need to have better undertsanding of how i can easily find out the TILDE approximation for any expressions.Please explain me with some examples including the following quantities.

N¹⁰⁰ / 2^{N ~ ?}

lg(2N) / lg(N) ~ ?

lg(N²+ 1) / lg(N) ~ ?

Note: No copy/paste from Google search please