 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2016/imperative-programming-resit/1/a/solution

Because

b > 1

b

is strictly increasing. The definition of the floor function gives

i \leq lo g_{b} n < i + 1

, so the equivalent characterization of the integer logarithm is

b^{i} \leq n < b^{i + 1} .

Here

i

n = 1

gives

i = 0

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