What does O(log n) mean exactly?

Question

I am learning about Big O Notation running times and amortized times. I understand the notion of O(n) linear time, meaning that the size of the input affects the g

Answer 1

log x to base b = y is the inverse of b^y = x

If you have an M-ary tree of depth d and size n, then:

• traversing the whole tree ~ O(M^d) = O(n)

• Walking a single path in the tree ~ O(d) = O(log n to base M)