Convert range of values to no linear range

Hello, could someone help me for a software I'm programming? I need to send float values from 0 to 1 that must be translated in "real world" values. Here is the example:

Freq (min and max):

0.000003 -> 20 Hz

0.5 -> 650.66 Hz

0.999997 -> 21168 Hz

Bandwidth (min and max):

0.00791 -> 0.010 8va

0.5 -> 2.007 8va

0.99997 -> 8 8va

As you can see, the scale is not linear. Does it exists a formula that can be used to convert the float value to the real one? Thanks.

Re: Convert range of values to no linear range

OK, I have found the answer for Frequency:

R = Range values

F = Frequency values

a = (Rmax - Rmin) / ( ln(Fmax) - ln(Fmin) )

b = Rmin - a * ln(Fmin)

R = a * ln(F) + b

But it doesn't work for Bandwidth. It works only when applied to max and min values. Any idea?