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Is there any difference between taking the logarithm of a quantity, and plotting a quantity in logarithmic scale?

Qmechanic
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Ana
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1 Answers1

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Yes, there will be a difference in how you label the axes. This sounds trivial, but loads of people get it wrong. Imagine you have a luminosity, measured in solar luminosities, on the y-axis of a graph.

If you plot it on a log scale, the label should read "Luminosity ($L_{\odot}$)" and equal steps along the y-axis will have numbers like 0.1,1,10,100 etc.

If you take logs of the data and then plot them, the label should read "$\log_{10}$ (Luminosity/$L_{\odot})$" with no units and the equally spaced numbers along the y-axis would be -1, 0, 1, 2 etc.

ProfRob
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  • I don't know if I would make such a distinction between the two plots. One plot contains a log of the data, and the other is the logarithm of a dimensionless form. In many instances, the dimensionless form is more general and useful. – David White Aug 06 '15 at 23:39
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    @DavidWhite "One plot contains a log of the data" - yes, that is the log of the dimensionless form. What is the meaning of the log of a dimensional form? The only distinction I am making is that the plots should be correctly labelled. For instance labelling the second plot as "$\log_{10}$ Luminosity" or $\log_{10}$ Luminosity ($L_{\odot}$)" are both incorrect. As is labelling the first plot anything but "Luminosity ($L_{\odot}$)" or Luminosity/$L_{\odot}$. – ProfRob Aug 06 '15 at 23:54
  • Hmm or you could label the first one "Luminosity" and then write the ordinal numbers as $0.1L_{\odot}$, $1L_{\odot}$ etc. – ProfRob Aug 06 '15 at 23:58
  • Anytime you have a ratio where there are the same units in the numerator as the denominator (e.g., luminosity/base-luminosity) your answer is just a number (it is dimensionless). And yes, I slightly misread your question above. The fact that you are plotting on a log scale eliminates the need to label the axis Log(luminosity), as you stated. – David White Aug 07 '15 at 01:57