How would I solve these problems involving time complexity:
Suppose we are comparing implementations of insertion sort and merge sort on the same machine. For inputs of size $n$, insertion sort runs in $8n^2$ steps, while merge sort runs in $64n \log_2 n$ steps. For which values of $n$ does insertion sort beat merge sort?
What is the smallest value of n such that an algorithm whose running time is $100n^2$ runs faster than an algorithm whose running time is $2^n$ on the same machine?
For each function $f(n)$ and time $t$ , determine the largest size $n$ of a problem that can be solved in time $t$, assuming that the algorithm to solve the problem takes $f(n)$ microseconds.
(a) $n! = 1$ second
(b) $n \log_2 n$ = 1 second