I am learning about Big O notation. I am looking at a problem in a book and it says, "Each of the following formulas for the number of operations is some algorithm. Express each formula in big-O notation."

a) n^2+5n

b) The number of digits in 2n

c) The number of times that n can be divided by 10 before dropping below 1.0

d)100n+5

my answers are:

a) O(n^2)

b) ??

c) ??

d) O(n)

the answer in the book for b and c are the following:

b) is logarithmic O(log n)

c) is quadratic O(n^2)

I don't understand b or c...