Gaussian curve, x is a log scale

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When applying a Gaussian function on a logarithmic scale, the resulting curve does not exhibit linearity, contrary to initial assumptions. The mathematical representation of the Gaussian curve changes to y = ae^{-(log x)^2} when x is on a log scale. This transformation indicates that the function's behavior is not linear, especially as the rate of change varies. The discussion highlights the misconception that a logarithmic scale could yield a linear approximation of the Gaussian function. Understanding these mathematical properties is crucial for accurate data representation.
nobahar
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Hello!
If I have the gaussian function, but x is a loarithmic scale. Can I infer that, if x was plotted using a regualr scale, that the function would be 'fairly' linear? At least initially? As the rate of change gradually increases befor slowing down again. I think this is reasonable... I don't know how to try and represent it mathematically.
 
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The Gaussian curve is
y= ae^{-x^2}
so if x is a log scale you have
y= ae^{-(log x)^2}[/itex]<br /> No, that is not a linear function.
 
Thanks Halls.
 

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