Past exam of the year 1 of the computer science course of the University of Oxford / 2016 / Imperative programming (resit) / 1 / a / Solution

Because $b>1$, exponentiation to base $b$ is strictly increasing. The definition of the floor function gives $i\le {\log }_{b}n<i+1$, so the equivalent characterization of the integer logarithm isHere $i$ is a nonnegative integer; $n=1$ gives $i=0$.