Solution #33

The sine function is bounded between -1 and 1, so we first consider when the monotonically increasing log function is in this range. We have:

-1 <= (log₂x)/5 <= 1
-5 <= log₂x <= 5
1/32 <= x <= 32

We then note that sin(5πx) has a cycle length of 2/5. So between 0 and 32, it completes 80 cycles. Because the log function is roughly horizontal, it will intersect a given cycle twice.

We now have to check the endpoints carefully. Because sin(5πx) is 0 at x =0, and increasing, we do not miss any intersections between 0 and 1/32. However, (log₂x)/5 is 0 at x = 2, where sin(5πx) is also 0. This means that we miss one intersection point, leaving a total of 159.