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Currently I'm making some plots for my colleted data set from my conducted physics experiment. In one of the cases, I'm actually plotting the logarithmic relation between the dependent and independent variable.

In this case, where I for instance have time as unit on my axis, I'd denote the units as [s] for seconds, but how do you write the units when you have "logarithmic time"? I hope my question was made clear enough.

Thanks!

Tanamas
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  • A logarithm is a pure number and has no units... – DJohnM Jan 22 '22 at 18:44
  • It depends. Are you plotting the logarithm of a quantity, or the quantity in a logarithmic scale? – Emilio Pisanty Jan 22 '22 at 18:51
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    @DJohnM That's not quite true. Logs are slightly different from the other transcendental functions due to the property log(A/B)=log(A)-log(B). A/B might be a dimensionless argument, such as when A and B have the same dimensions. However, because of the quotient-difference rule above, it is algebraically valid to write the term log(A). If A has units, then it is not quite true that log(A) has no units. – electronpusher Jan 22 '22 at 19:24
  • Related: https://physics.stackexchange.com/questions/364771/why-is-it-bad-taste-to-have-a-dimensional-quantity-in-the-argument-of-a-logari and links therein – Emilio Pisanty Jan 22 '22 at 19:45

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You could show the actual numbers (e.g., $10^3$, $10^4$) and label the axis as “time [s]”, or you could plot the logarithms (e.g., 3, 4) and label the axis as “$\log_{10} \frac{\mathrm{time}}{1\ \mathrm{s}}$ [unitless]”. Some people will abbreviate this as “log(time) []” and figure they’ll be understood.

Chemomechanics
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