Problem of the Day #60

POTD February 3, 2024

Let A = (a, \log_2 a), M = (m, \log_2 m), and B = (b, \log_2 b) be three points on the graph of y = \log_2 x, where 0 < a < m < b. Let points P and Q be on segment AB such that MP is parallel to the y-axis and MQ is parallel to the x-axis. Given that AP=PQ=QB, \frac{b}{a} can be expressed in the form j+k \sqrt l, where j,k and l are positive integers and l is not divisible by the square of any prime. Find j+k+l.