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?
