What are the scaling exponents and log bases

Documentation simply states “you can also select from two exponential and two logarithmic scales.” (taken from the hydra description)

I’d guess the log bases would be common, such as e and 10. Can’t venture a guess on the exponents. Any clarification would be wonderful. Complete clarification would be even better :)

bumped. i’m confused why this info wouldn’t be in the documentation.

Anybody? Dev needed of course; I’m not just curious, knowing the values is necessary for me to achieve a mathematically accurate result via meta-device parameter automation.

I’ve been reverse engineering the various scales in the current version (2.8.1).
Still trying to work out the log-based ones.
The notation used is that x is normalized input, i.e. 0 <= x <= 1, and f(x) is normalized output, i.e. 0 <= f(x) <= 1.
Here’s what I have so far:

“Steep” exponential:
f(x) = (e^(ln(16)*x^2) - 1) / 15

“Soft” exponential:
f(x) = (e^(ln(16)*x) - 1) / 15

with x = 0 to 1, s = 0.1 or 0.2 or 1.0 or 2.0  
y = exp(log(16)*pow(x, s))/15 - 1/15  

Plot on Wolfram alpha: http://www.wolframalpha.com/input/?i=plot+y+%3D+exp(log(16)+*+pow(x%2C+s))+%2F+15.0+-+1+%2F+15%2C+x%3D0..1%2C+s%3D1