Forgive my ignorance here. I am referring to logarithm base 1 which is undefined (https://arbital.com/p/log_base_1/)
I am learning the time complexity in programming and logarithm in mathematics.
Logarithm base 2 of 32 is 5, and if I correlate that to the time complexity to find an element in a sorted array of 32 elements using binary search, it would at most take 5 steps to find the target element using binary search, which is O(log₂ n). Also, according to my understanding of logarithm, if I split the array into 3 parts to search the target element, it should be a ternary search instead of binary search and the logarithmic complexity would be of base 3 instead of base 2 which is O(log₃ n), and in all cases, n = 32 because that's the number of elements in the array here.
Now, in mathematics, the logarithm base 1 is undefined, but if apply the above analogy and do a search for a target element in the same sorted array mentioned above, but without splitting at all, it would equate to O(log₁ n) (this is my assumption here) which practically would be O(n) and linear. So shouldn't (log₁ n) = n?
I was referring to the Ternary search as explained here https://www.hackerearth.com/practice/algorithms/searching/ternary-search/tutorial/#:~:text=Like%20linear%20search%20and%20binary,which%20part%20the%20element%20exists.
Thanks in advance.