Formulas for calculating how many f-stops between two different shutter speeds

4 stops means a 16x change in light (i.e., 1/8 --> 1/125)

2⁴=16

125/8= 15.625    (approximately 16 because of rounding errors in listed shutter speeds)

Let x = number of stops difference, and y equal the slowest shutter-speed divided by the fastest.
To find the exact number of stops in 2^x=y

x=log^-1((log(y))/2

Example:
In the 1/8 to 1/125 example listed above, 1/8 divided by 1/125 equals 15.625

x = log^-1((log(15.625))/2 = log^-1(1.19382/2) = 3.95 stops