Understand function slope in log-log space

Mike82

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Jan 27, 2018
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Hi math experts - trying to kick start my old math and log skills.

A8467FC0-4639-4AA2-9127-09D3227C5D2D.jpg

In the attached screenshot from Wikipedia the sRGB transfer function x^2.2 is plotted in log-log space (blue slope). How do I interpret interpret the y axis from the x values in the example?

Also, in general what are the main applications for log-log space plots?

Need to do my homework but hope for a pointer in the right direction.

Thanks,

Mikael
 

stapel

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View attachment 9065

In the attached screenshot from Wikipedia the sRGB transfer function x^2.2 is plotted in log-log space (blue [curve]). How do I interpret interpret the y axis from the x values in the example?
For what do the x-values stand? For what do the y-values stand? (I can't read the graphic; it's too tiny on my screen. Sorry.)

Also, in general what are the main applications for log-log space plots?
For linearizing stuff that's growing fast (as, for instance, is illustrated here). You may find the articles in this listing to be helpful. ;)
 

Mike82

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For what do the x-values stand? For what do the y-values stand? (I can't read the graphic; it's too tiny on my screen. Sorry.)


For linearizing stuff that's growing fast (as, for instance, is illustrated here). You may find the articles in this listing to be helpful. ;)
Thanks! See https://ibb.co/ddZx1w for high-res, my iphone must have screwed up the initial image 😬 x/y values better now?

Will take a look at the links!


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stapel

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Thanks! See https://ibb.co/ddZx1w for high-res, my iphone must have screwed up the initial image 😬 x/y values better now?
It looks like they're talking about monitor displays, RGB profiles, and gamma curves, which is all imaging stuff that's over my head. Maybe another helper is into that, and can explain what they're talking about.
 

Mike82

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It looks like they're talking about monitor displays, RGB profiles, and gamma curves, which is all imaging stuff that's over my head. Maybe another helper is into that, and can explain what they're talking about.
Skip the imaging, the x values gives x^2.2 on the right y axis while the left y axis is the same slope plotted in log-log space.

So if I get things right, the right y scale is the log scale of the linear x axis for x^2.2?


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