What is Logarithmic scale: Definition and 15 Discussions

A logarithmic scale (or log scale) is a way of displaying numerical data over a very wide range of values in a compact way—typically the largest numbers in the data are hundreds or even thousands of times larger than the smallest numbers. Such a scale is nonlinear: the numbers 10 and 20, and 60 and 70, are not the same distance apart on a log scale. Rather, the numbers 10 and 100, and 60 and 600 are equally spaced. Thus moving a unit of distance along the scale means the number has been multiplied by 10 (or some other fixed factor). Often exponential growth curves are displayed on a log scale, otherwise they would increase too quickly to fit within a small graph. Another way to think about it is that the number of digits of the data grows at a constant rate. For example, the numbers 10, 100, 1000, and 10000 are equally spaced on a log scale, because their numbers of digits is going up by 1 each time: 2, 3, 4, and 5 digits. In this way, adding two digits multiplies the quantity measured on the log scale by a factor of 100.

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  1. DaveC426913

    B How does one draw a logarithmic scale?

    So I'm playing with this visualization from this other thread and I'm brute-forcing the "days" scale because don't really know how to place the marks. (by brute-forcing, I mean I am using SUVAT to calculate the distance one can travel in one day, then redoing it to calc the distance in two...
  2. FEAnalyst

    I Logarithmic scale - interpolation

    Hi, knowing the coordinates of two points: ##(x_1,y_1)## and ##(x_2,y_2)## on a linear scale plot, I can use linear interpolation to get ##y## for a point of known ##x## using the formula below: $$y=y_1+(x−x_1) \frac{(y_2−y_1)}{(x_2−x_1)}$$ But how does it look like in the case of logarithmic...
  3. T

    B Why is an inverse logarithmic scale chosen for the magnitudes of stars?

    Star magnitudes of brightness seem to use inverse logarithmic scales, is there a benefit to this? Why was this chosen, i can understand logarithmic might make it easier to interpret data in same way we do similar for earthquakes etc. But why inverse ? When i look at a HR diagram for example (...
  4. scottdave

    B Using a logarithmic scale to represent COVID-19 growth

    The author, John Burn-Murdoch, shows here ( https://threadreaderapp.com/thread/1237748598051409921.html ) how the logarithmic scale can give a better "sense" of what is happening. In linear scales, some countries' data is squashed to almost nonexistent, while others explode out of control. I...
  5. L

    MATLAB How to transform a plot to use a logarithmic scale?

    I wrote the following code in MATLAB: t = [0:0.001:0.1]; noise = randn(1,size(t,2)); a = 15*10^9; b = 15*10^(-3); c = 7*10^8; y = a*exp(-t/b)+c+noise*100000000; fun = @(p,t)p(1)*exp(-t/p(2))+p(3); p0 = [15.5*10^9, 14*10^(-3), 6*10^8]; p = lsqcurvefit(fun, p0, t, y); t_fit = [0:0.0001:0.1]; y_fit...
  6. Leonardo Machado

    How do I create a logarithmic scale graph and determine line spacing?

    Hello every one. Today's question is: if I'm writte a graph using logarithm scale, must i use the dimensions of the graph "logarithmized" too ? i.e : A Distance x Force graph must have its dimensions as log (m) x log (N) ? or it is just valid for the module ? Thanks for the tips
  7. A

    Logarithmic scale for the Laser Intensity.

    I drawed a relation between the growth rate of the material to the laser intensity. After drawing, My professor told me that I must convert both values of the growth rate and the laser intensity to their values in the logarithmic scale. I don't know how. May I get a help.
  8. N

    Calculating time in a logarithmic scale

    Hi Everyone, I have a question about logarithmic sampling. I think I might have to go and review my Z-transforms, but maybe not. The reason I am doing this is because I am automating equipment which records the data over time, but I want the sampling to be done logarithmically. If I have an...
  9. C

    Logarithmic Scale: What Happens When Plotting x,y Values?

    Hello people, I have a question about the log-scale. What happens when we switch a plot from linear scale to the log scale? Let's say I have two arrays: x values and corresponding y values. I plot them using a linear scale and then I switch to the log scale. What happens? Does the program...
  10. A

    Exploring the Relationship Between Inverse Variables on a Logarithmic Scale

    Let me start by saying my understanding of logarithms is relatively limited, with that out of the way on to my question. The question I have is in a situation where you have 2 items that are inversely related and both have a starting point of 100%. How would you calculate the point where...
  11. B

    Calculating the gradient of a logarithmic scale

    Homework Statement hi i have the folowing data i would like to plot in matlab plotERRLW = 0.0466 0.0111 0.0074 0.0046 NX = 50 500 1000 2000 i am using a logarithmic graph to gain a straight line, if i wished to find the gradient of the line...
  12. J

    Linear to logarithmic scale conversion

    Hi! I'm making a computer program that represents some quantities in a graph in this way: x'i=(xi-xmin)/(xmax-xmin) so that the possible values of x range from 0 to 1. This is a linear scale. I want to do the same with the logarithmic values of xi. That is, I want to implement a log...
  13. J

    Logarithmic Scale: Calculating Evenly Spaced X Values

    Hello All, I am working on a program that produces plots that use a logarithmic scale on the X-Axis (for showing decade frequency ranges). The Y-axis can have any arbitrary value and I'm not thinking about that at this point, but here is my question. Say, for simplicity that every Y-value...
  14. M

    Sound intensity is measured on a logarithmic scale

    Help please! Here is the prob and i don't not know where or how to begin. 1.Jose was having a really bad day out on the bike. He should have checked the forecast. First, the wind coming out of nowhere. Must have been a steady 30 mph with gusts up to 50, head on. Then the lightning. First 1...
  15. L

    What is the issue with log scales and plotting values less than 1?

    I am working on a homework for a programming class. We have to create a Logarithmic plot and add to it a marker when the program is running on the click of the mouse. That is NOT the problem :) , in fact, that's very simple! My problem, however, is with the scale. When my plot is in linear...