Question

Find the appropriate "order" relationship between n log(n) and 10n and find the constants c and N.

(i.e. f(n) < O(g(n)), etc.)

Answer 1

If N >= 2^10,
then, taking log on base 2 both sides:

log(n) >= log(2^10)
which can be written as:
log(n) >= 10

Multiplying by n on both sides:

n Log(n) >= 10n

Or
10n <= n log(n)

Hence We can say, 10n = O(nLogN)
Hence, N = 2^10, and c = 1

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