Linear to logarithmic scale conversion

[jocasa]

Hi!

I'm making a computer program that represents some quantities in a graph in this way:

x'_i=(x_i-x_min)/(x_max-x_min)

so that the possible values of x range from 0 to 1. This is a linear scale. I want to do the same with the logarithmic values of x_i. That is, I want to implement a log scale in my graphs, also in the range from 0 to 1.

Can anyone tell me how to do it?

Thanks!

 

[berkeman]

Hi!

I'm making a computer program that represents some quantities in a graph in this way:

x'_i=(x_i-x_min)/(x_max-x_min)

so that the possible values of x range from 0 to 1. This is a linear scale. I want to do the same with the logarithmic values of x_i. That is, I want to implement a log scale in my graphs, also in the range from 0 to 1.

Can anyone tell me how to do it?

Thanks!

Welcome to the PF.

What language are you programming in? Does it have any math libraries that cover logarithms?

 

[jocasa]

I'm using C++ and it has both log and log10 functions, that is, log in base e and log in base 10.

I'm not sure if I made myself clear in my first post. I want to be able to make log-log plots, transforming the resulting plot into the [0,1] interval.

 

[Redbelly98]

Hi!

I'm making a computer program that represents some quantities in a graph in this way:

x'_i=(x_i-x_min)/(x_max-x_min)

so that the possible values of x range from 0 to 1. This is a linear scale. I want to do the same with the logarithmic values of x_i. That is, I want to implement a log scale in my graphs, also in the range from 0 to 1.

Can anyone tell me how to do it?

Thanks!

I think this will work:

x'_i = (log(x_i)-log(x_min)) / (log(x_max)-log(x_min))​

As a test, we can see that if x_min,max are 1 and 100, then x_i=10 gives x'_i=0.5. As it should, since 10 is halfway between 1 and 100 on a log scale.

 

[jocasa]

Thanks! It makes sense to me. Now the problem is to implement it in the program, but I won't bother you with such a thing. Thanks again from Spain!