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I have some data which produces the following logarithmic curve. As you can see, the curve produces the exact opposite of what Im trying to achieve (my data is the line with dots, the logarithm is the light blue line). Do I need to turn it into an exponential? Do I need to find the antilog of this equation and if so any ideas on how I might go about this? Is there a way of reversing a logarithm?

enter image description here

Logarithm Regression y = α * ln(x) + β

α: 8.10790887182717 β: -16.816261044713226

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    $\begingroup$ It appears to be an exponential. $\endgroup$ Apr 15, 2014 at 7:29
  • $\begingroup$ Yes, ive tried to do logarithmic regression on it and exponential regression, but the logarithmic one seems to fit the curve much better. I was thinking to use the logarithmic one and then reverse it. However, do you think it's best that I work on getting a better exponential fit? $\endgroup$
    – Ke.
    Apr 15, 2014 at 7:31
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    $\begingroup$ Have you tried $y=A B^x+C$? $\endgroup$ Apr 15, 2014 at 7:34
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    $\begingroup$ It cannot be a logarithm regression. For $x=0$, you have $y=0$. As said by Martín-Blas Pérez Pinilla, the curve looks more like an exponential. Consider something such as $y=-1+a e^{bx}$. You could check if this is stupid plotting $\log(y+1)$ as a function of $x$. If this looks as a straight line, continue. $\endgroup$ Apr 15, 2014 at 7:34

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What you want, what in fact is the "inverse of the logarithm", is an exponential function $$y = P \cdot Q^x$$ for constants $P,Q$. However, you may also need to adjust it in the y-direction (it's hard to read the exact coordinates of your data), so if the above fails try to adapt a curve for $$y = P \cdot Q^x + R$$ for constants $P,Q,R$.

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  • $\begingroup$ just checking, is p = a and q = b? Also im wondering what R stands for? $\endgroup$
    – Ke.
    Apr 15, 2014 at 7:59
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    $\begingroup$ Yes, coefficients a and b may be more common, but it's not the values a and b that you calculated for the logarithmic regression. R, in this case, adjusts the calculated regression along the y-axis. $\endgroup$
    – naslundx
    Apr 15, 2014 at 8:04

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