I'm given the problem: For x amount of elements, plot the time complexity (Big-O) of binary search vs linear search. What I don't understand is what base the time complexity of binary search should be. Given that log base 10 and 2 give different graphs for any x. I know that base doesn't matter for Big-O notation. But what do I need to consider when plotting this graph when determining time complexity advantage of binary search compared to linear search?
It matters I think because let's say we have 20,000 elements in our array. Then linear search takes 20,000 operations. But should it be for binary search $20,000\div\log_2(20,000)\approx1399 $ faster or $20,000\div\log_{10}(20,000)\approx 4650$ times faster?