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I have a given set of data points (y,x) with uncertainties.

When I plot those points on a graph, the trendline appears to follow the equation y = c + a*ln(x).

I want to be able to find the uncertainty in "a".

So just like linearizing an exponential function $y=e^{ax}$ as $\text{ln}(y) = ax$, and we can get the uncertainty in "a" by graphing the minimum and maximum slopes and averaging it out,

Is there a way to linearize a logarithmic function $y=a \text{ln}(x)$ ?

Thank you.

EDIT: Link to duplicate answer in comments.

선풍기
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  • Not sure what you might mean by "linearize". What's wrong with $e^{y/a}=x$? – lulu Feb 10 '18 at 17:45
  • I have a given set of y and x which has a logarithmic relationship, and I need to find "a". – 선풍기 Feb 10 '18 at 18:15
  • Ok, why not take $a=\frac y{\ln x}$ then? – lulu Feb 10 '18 at 18:18
  • Sorry if I was unclear; I have a given set of data points (x, y) with uncertainties, and when I plot them on a y vs x graph and draw a trendline through it, I get an equation that is like y=c+a*ln(x). I want to be able to find the uncertainty in "a". – 선풍기 Feb 10 '18 at 18:22
  • Please edit your post to ask a clear and coherent question. – lulu Feb 10 '18 at 18:23
  • Yes, should have done that earlier – 선풍기 Feb 10 '18 at 18:27
  • Found the answer while digging: https://math.stackexchange.com/questions/181844/least-squares-fitting-logarithmic See Robert Israel's Answer – 선풍기 Feb 10 '18 at 18:43

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$$y = a \ln x \implies e^{y/a} = x $$

Mark Fischler
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