Scaling Y-Axis by natural log scale.

Hi,

I need to scale my Y-Axis by a natural log scale to apply the hvorslev method to calculate hydraulic conductivity of my sampled sites. Is there anyway to go about doing that in MATLAB ? I have dug up several documentation for doing log plots in MATLAB but none of them seem to allow for a natural log scaling. (Semilog is in log10, changing the axis in the plot function only allow for log10 ...)

Answer 1

[Voss]

log10 scale is the same as natural log scale is the same as log2 scale is the same as log-any-base scale.

Logarithmic scale means that two numbers whose ratio is a given value are the same distance apart (as opposed to linear scale which means that two numbers whose difference is a given value are the same distance apart). For instance, 20 is 2 times 10, and 10 is 2 times 5, so the distance from 5 to 10 and the distance from 10 to 20 will be the same on logarithmic scale.

semilogy(1:100)
yline([5 10 20],'r') % 10-line is halfway between 5-line and 20-line

semilogy(1:100)
yline([1.25 2.5 5 10 20 40 80],'r') % all equally spaced because the ratio is two from one to the next

Those lines are at a ratio of two between them. Does the factor of 2 have something to do with log10 scale? No, it's not special. Let's pick a ratio of 3 instead.

semilogy(1:100)
yline([1 3 9 27 81],'r') % all equally spaced because the ratio is three from one to the next

semilogy(1:100)
yline([1.4 4.2 12.6 37.8],'r') % all equally spaced because the ratio is three from one to the next

How do you think the plot should look different if it were "natural log" scale?

[Quentin 'Quinn']

The space in between each "equal ratio" spacing will be scaled by a factor of e ?

[Voss]

You can draw lines at powers of e, but the y-axis scale is still the same as before

semilogy(1:100)
yline(exp(1:4),'r')

You can put the tick marks at powers of e:

semilogy(1:100)
yticks(exp(1:4))
set(gca(),'YMinorTick','off')

And adjust their labels:

semilogy(1:100)
yticks(exp(1:4))
yticklabels("exp("+(1:4)+")")
set(gca(),'YMinorTick','off')

Is something like that what you have in mind?