Method to compute a logarithmic value within a specific range

Asked Jan 11 '18 at 13:08

Active Jan 11 '18 at 13:08

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Hello I'm trying to create a formula that returns the y from the graph image below. It's always within a range. For example (0.5 - 2) for any x value.

The closest I've been to is: 1 /(1/log2 (x) ) ^ 2 + 0.5 (min range value)

Whose graph looks like this:

But I need something like this:

asked Jan 11 '18 at 13:08

Alexandru R

$$f(x)=\dfrac{5\cos x-3}5$$ – lab bhattacharjee Jan 11 '18 at 13:11
1

If you can do without the logarithms, that hand-drawn curve looks logistic. Try playing around with $\dfrac a{b+e^{cx}} + d$. For instance, $\dfrac{1.5}{1+ e^{2x}} + 0.5$ – Arthur Jan 11 '18 at 13:13
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Another option is a hill type function $-x / (k + x)$ – Sort of Damocles Jan 11 '18 at 13:18
I didn't know about logistic curves, looks very similar to what I need – Alexandru R Jan 11 '18 at 13:21

Method to compute a logarithmic value within a specific range

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