How can you mathematically represent the performance of Line

How can you mathematically represent the performance of “Linear Search” and “Binary Search”?

Solution

Binary Search

log₂(2^x)    = log₂ N
x * log₂(2) = log₂ N
x * 1         = log₂ N

Linear search

n if k=0
(n+1)/(k+1) if 1<=k<=n