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From the textbook 'Brock biology of microorganisms, 15th edition'

The black lines points to the linear graph with the caption 'Logarithmic' and to the curved graph with the caption 'Arithmetic'. Isn't this the reversal of what they are?

  • 1
    $\begingroup$ No it's correct. The arithmetic plot uses the left side of the graph and if you take the log of the values on the arithmetic plot (log10) it'll plot out a straight line; the red one which use the right side as the y-axis. $\endgroup$
    – m4rio
    Commented Jun 13, 2021 at 8:11
  • $\begingroup$ To add to @m4rio's comment: As someone once said "biochemists worship at the alter of the straight line" (It is the logarithmic plot that is linear, as is the Lineweaver-Burk plot, the Eadie-Hofstee plot, the Hanes plot, and quite a few others: they are all linear transformations of non-linear 'primary' plots) $\endgroup$
    – user338907
    Commented Jun 13, 2021 at 9:19
  • $\begingroup$ It's always a good idea to carefully examine the numbers on the axes and draw your own conclusions before looking at the labels. $\endgroup$
    – Armand
    Commented Jun 13, 2021 at 13:28

1 Answer 1


The image is correct, although the presentation is confusing because the association of the lines with the axes is not indicated clearly.

Plotting on an arithmetic scale (the "normal" sort of axis we all first learn about), an exponentially growing number of cells will result in a line that starts out looking pretty flat and then suddenly shoots up.

If you're interested in knowing the rate of growth, this sort of line isn't very useful, because the same rate will have different slopes, while the same slope indicates different rates, depending on the number.

If you instead plot the growth curve against a logarithmic axis, then you get a graph that focuses clearly on growth rate, with the same slope always indicating the same rate, no matter how many cells are present. Thus, if the growth rate is consistent, you'll see a straight line, as in the example presented.


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