Scale increase and decrease?

Question

Mathematics

Hello. Already the whole brain has broken, I just can’t come up with a formula. Can you tell me ;)
I'm making a slider to increase and decrease.
Start 0.
Minimum value -10
Maximum value 10
Uncompressed image 1 - on slider 0
Decrease by 10 times, so 1 / 10 = 0.1 - on slider -10
Decrease by 2 times, so 1 / 2 = 0.5 - on slider -5
Increase 10 times - on slider 10
Increases 5 times - on slider 5 It
's not clear what to do in 1 and -1, how to beat them?
Thank you.

Answer 1

You need a logarithmic scale. The zero of the scale will correspond to scale 1. If the scale is 10, then we must take the scale 10 ^ (x/10), i.e. 10 if -10 then 10^(-x/10) = 10^(-10/10) = 0.1.
With x = 5 => 10 ^ (5/10) ~ 3.16
With x = -5 => 10 ^ (-5/10) ~ 0.316
With x = 1 => 10 ^ (1/10) ~ 1.259
With x = -1 => 10^(-1/10) ~ 0.794