I've taken a series of photos as a bracketed HDR, starting at 1/4000th of a second going up to 1 second. How many stops are there between those? How would you be able to tell?
The aperture and ISO do not change
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Algebraically, we want to to solve the following equation:
2n = 1 / (1 / 4000)
Taking log2 of both sides, we get
n = log2(1 / (1 / 4000))
n ≈ 12
Indeed, shutter speeds are supposed to be powers of two, so 1/4000 should actually be 1/4096 (that is, 1/212); they're just rounded to make them more human-friendly.
According to the table on this page, it's 12 stops.