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I'm still trying to wrap my head around logs and figuring out how to derive formulas from given value pairs.

In this example, at a value of 0.2:5mil should be derived, and at 1:1mil (so it's an inverse scale?).

How can I find out the output for a given value, say 0.1?

Basically, the closer the value gets to zero, the higher the output should be.

I came across these two questions which are close to what I'm looking for but I'm still having trouble deriving these formulas.

Any help is very much appreciated.

Microsis
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  • What do you mean by 0.2:5mil?What do you mean find out the value for a given value, say 0.1? The value is 0.1. I don't understand your question at all. – Ross Millikan Aug 15 '19 at 05:04
  • So as I interpret this, you're essentially looking for a function $f(x)$ that has the following properties: $$ f(0.2) = 5\cdot 10^6 \qquad \text{and} \qquad f(1) = 10^6 $$ $$ \lim_{x \to 0^{+}} f(x) = +\infty $$ And also the function should have something to do with logarithms. If not for the logarithm part, the simplest function that fullfills these requirements is $$ f(x) = \frac{10^6}{x} $$ Question: should the output always be positive? – Matti P. Aug 15 '19 at 05:16
  • @MattiP. thanks. It looks like the linear function (10^6/x) may work. However, playing with the numbers it seems like instead of f(1), I'll need f(10) = 10^6. Can I ask how you derived the formula so I can play with different values? – Microsis Aug 15 '19 at 14:15
  • @MattiP. and yes, always should be positive. – Microsis Aug 15 '19 at 22:58
  • At this point it's important to decide what form you want the function to have. On one hand, you mentioned that the form $f(x) = 10^6/x$ seems fine, and that's of the more general form $$ f(x) = Cx^{\alpha} $$ But this has nothing to do with logarithms, which was your wish in the post. Another form that is a bit similar and has to do with logarithms, would be $$ f(x) = Ce^{kx} $$ So which one would you prefer? It pretty much comes down to what you want $\lim_{x \to 0^+}f(x)$ to be (finite or infinite). – Matti P. Aug 16 '19 at 05:24
  • @MattiP. Great question that I didn't consider before. Basically, the output is a threshold that determines whether a stock is "liquid" enough. In other words, the lower the given price, the higher the volume required to determine it "liquid" -- Given that, I assume the output should be finite, capped at 10M or so, however I would need to play with live data to see if that's the limit I want to set. Thanks for your continued help with this. – Microsis Aug 17 '19 at 17:43

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