Finding a function that goes through given points

[iScience]

Homework Statement

Find a function of a decaying logarithmic trend that passes through a set of 3 points (at x=1,2,3) whose sum is S, where S>0.

Homework Equations

The Attempt at a Solution

starting point: i assumed the equation had the form: $$y= -kln(x+1)+S$$ with the condition that must satisfy:

$$S=Σ(y(x))$$ from 1→3

but I don't know what to do next

 

[haruspex]

In your proposed generic form, I see no reason to choose x+1 rather than x+an unknown constant. And I don't understand the final S; did you mean this to be the same as the given S or something different?
If we make it x+c as well as a final +d (say) then we have three unknowns (c, d, k) but effectively only one equation. So presumably the question expects a simpler generic form, but it is not clear what. If I had to guess, I would ditch d first.

Edit:After a little background reading, seems like you should keep d and ditch c. Logarithmic decay appears to be defined as the functional inverse of exponential decay, i.e. x=Ae^-ky.

 

[iScience]

I see no reason to choose x+1 rather than x+an unknown constant.

Oh, no actually not necessary, I was just trying to find a convenient way to set up the graph on my calculator; my proposed form would have essentially looked like the same graph as that of x=Ae^(-ky)

I don't understand the final S; did you mean this to be the same as the given S or something different?

Same S.I tried your suggested formula. Since the A was left as a free variable to be determined, i had two equations two unknowns and was able to solve. much thanks!