you can get something that is roughly the same shape by using a power inbetween 1 and 2.
Powers inbetween give you something that looks like the above plot.
no, it's not possible, even if you shift and scale the logarithm.
the more useful question is why do you even want to use a logarithm? and why specifically the natural log?
if it disabled accel completely, it'd be the same as setting accel=0, and would therefore be redundant.
so you are getting the base sens at low speeds
it should be noted though that you're not supposed to set the power to 1 in the first place
the power should only be set to values >1. Typically values around the default of 2 are nice.
full formula above, with the conditions that the accel term is bypassed when accel is zero or the speed is below the offset
when (v-c) is less than or equal to zero, the accel and power is skipped completely
I must be a blind, but it doesn't explain why I get lower sens if P=1 and c=100 compared to if P=1 and c=0
...Is not evident in the formula...
with c=100 you are NOT getting the +1 effect, as the accel term is skipped completely.
-x^0 = -1
when (v-c) is less than or equal to zero, the accel and power is skipped completely, so you are getting the base sens at low speeds.
the accel term is bypassed when accel is zero or the speed is below the offset
(positive) accel will never cause the base sens to be reduced
you will get +1 when v>c and +0 when v<c. as you raise c, you're less likely to get this +1 effect with a typical mouse speed.
because v isn't constant