Hi Boner,
The FV-1's LOG instruction implements the function
LOG(x) = K/16 log2(x) + C
with K in [-2, 2) and C in [-1, 1). When K = 1 and C = 0, LOG maps [0, 1) → [-1, 0], and the largest value it can output is 0. More generally it maps [0, 1) → [-K+C, C], and you can trivially solve for K and C to get your desired output interval. To your end, mapping the interval [0, 1) back to itself is achieved by setting K to 1 and C to the largest positive offset 0.999 ≈ 1.