-2

This may be a very simple question, but I haven't been in touch with Algorithms since a while.

I have a logarithmic scale of 20,100,500,2500,12500 which relates to 1,2,3,4,5 on the respectively. Now, I want to find out as to where the value 225 would lie on the scale above? And also, going the other way round, how would I find out as to what the value for 2.3 interpret to on the scale. Would be great if someone can help me with the answer and explanation for this.

Onkar Kuncolienker
  • 21
  • 1
  • 2
  • 2
    I'm voting to close this question as off-topic because it is about [math.se] instead of programming or software development. – Pang Aug 10 '16 at 02:46

1 Answers1

0

Note that each step in the scale multiplies the previous step by 5.

So the explicit formula for your output is

y = 4 * 5^x

or

x = log-base-5(y/4)

where

log-base-5(n) = log(n)/log(5)

if you want to compute it in code. That last line is called the change of base formula, and is explained here You can use either a natural log or common log on the right side of the formula, it doesn't matter.

roderick young
  • 284
  • 1
  • 10
  • Thanks a lot Roderick for your quick response on this! Its helpful :) – Onkar Kuncolienker Aug 09 '16 at 16:14
  • Sorry to bug you again, but how would I go about doing the same thing for 0.3,1,4,20,110 which would align to 1,2,3,4,5? This example doesn't have the simple multiplication of 5 as the previous example!. Maybe it uses a square log function? – Onkar Kuncolienker Aug 09 '16 at 17:47
  • Perhaps it would be best to ask curve-fitting questions on a math.stackexchange.com as the person above suggests. They will have a lot of good suggestions. One idea is to the a log of each output value, log(0.3), log(1), log(4), and so forth. Then plot them on a graph. If they're in a straight line, then the function can be represented by something like a * e^(bx), where a and b are not necessarily integers. By the way, if you delete this question that they don't like, you will get a badge for it. Don't feel bad about getting voted down, it's nothing personal. – roderick young Aug 11 '16 at 00:38