My friend got asked this question during his interview with Netflix!

Imagine that you have an infinite sorted list of words. Assuming that your word of interest (targeted_word) is at the K position (K is very large). You start at the position x (x less than k). If word[x] < targeted_word, then you move x/2 position, i.e. x = x + x / 2. What is the complexity in term of K. If it is in a log form, then what is the base of the log.

I'm not sure whhat is the right answer here!