Which is faster: linear or logarithmic complexity?

Logarithmic complexity is faster than linear.

Justification:

Logarithmic complexity O(log n) grows much more slowly than linear O(n) as the size of input data n increases.

Examples:

• Searching for an element in a sorted array using binary search has logarithmic complexity O(log n).
• Searching for an element in an unsorted array by checking all elements has linear complexity O(n).

Growth chart:

n	log₂(n) (approximate)	n
1	0	1
10	3.3	10
100	6.6	100
1000	9.9	1000

As seen from the table, as n increases, log₂(n) grows significantly slower than n. This means that algorithms with logarithmic complexity will execute faster, especially on large datasets.