what is the big O complexity of the functions involving log

Question

what is the big O complexity of the function 1005 n^1.75 + 100 n^1.5 + 10nlogn ?

I know that the big O complexity of logn is equal to O(logn)^2) but can't figure out this riddle: 1005 n^1.75 + 100 n^1.5 + 10nlogn

Answer 1

f(n) = 1005 n^1.75 + 100 n^1.5 + 10nlogn

Now, in O notation, we only need to consider the highest order terms, also constants can be ignored. Therefore,

f(n) = n^1.75

Hence,

O(f(n)) = O(n^1.75) or O(n^7/4)

Answer 2

the complexity of that function is:

O(N^(7/4))