What is Log scale: Definition and 12 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. bob012345

    Milestones of a human lifetime on a log scale

    In another thread the concept of how many seconds in a year came up and it made me think of putting milestones of a human lifetime on a log scale. Units are seconds. Please feel free to amend or change or just make it better. Maybe an actual plot? What strikes me is most of life is in the last...
  2. W

    Log-Plots: Solving Homework Equations

    Homework Statement Homework EquationsThe Attempt at a Solution I have been trying to rearrange the equation to look something like ln(y) = Aln(x) but to no avail. Something tells me that that's not necessarily the right way to approach the problem, could anyone point out what I should be...
  3. A

    Fortran How to change data from linear scale to log scale

    I am trying to calculate and draw a relation between (IL) and the Growth rate (m). I have used Il as range from 10^15 to 10^18 in the calculation and when I draw the relation (x-axis ) is Il and (y-axis ) is m. I converted the IL to be in log scale. I noticed unacceptable output. So, I am...
  4. P

    Benefits of Joining the PF Community as a Biologist

    Hi everybody, Looking forward to be part of this community! A biologist here trying to become more math savvy and willing to help others too.Thanks,
  5. L

    Kinetic Energy - use a log scale or not?

    Homework Statement Lets say we have a series of balls and an eggs. All items have equal mass but are traveling at different velocities. Thus they have differing kinetic energies. Now, for each 'ball' object we have, we want to find an egg object with a similar kinetic energy. Let's say...
  6. Aristotle

    Angular Velocity and Position: How to Solve Basic Angular Motion Problems

    Homework Statement Homework Equations ω=ω0+αt θ=θ0+ω0t+12αt2 I think? The Attempt at a Solution For part a, I know that from the graph, the angular velocity in this case would be constant since the graph illustrates a position in rad vs time graph. The thing is, I'm really sure on how to...
  7. G

    True Stress-Strain Curve on the Log Scale: Which portion is the plastic region?

    My math is a little weak, so I'm having a hard time finding the elastic and plastic regions on this curve. Any further help will also be appreciated!
  8. M

    Estimating area under a curve in log scale

    Homework Statement Hi guys, I'm stuck on this question in exam revision: I need to estimate the area under the following curves (I don't have the equations of the curves) http://img819.imageshack.us/img819/3249/question.jpg The curves are magnitude diagrams in the log-log scale...
  9. N

    Gaussian curve, x is a log scale

    Hello! If I have the gaussian function, but x is a loarithmic scale. Can I infer that, if x was plotted using a regualr scale, that the function would be 'fairly' linear? At least initially? As the rate of change gradually increases befor slowing down again. I think this is reasonable... I...
  10. R

    Data weighting on semi log scale

    Hi I have to perform a fitting procedure on a semi logarithmic scale but I'm not sure how to weigh the experimental data points. I'm studying the decay of the luminescence of a certain type of crystals and the function I'm using has the form I = \frac{1}{\tau} e^{-\frac{t}{\tau}}...
  11. P

    Mathematica ParametricPlot and log scale axes in Mathematica

    Hello, I have been trying to make a parametric plot with logarithmic axes in Mathematica, but have been unable to find an option to do this. Can someone tell me how to do this? My code is below, and for reference, EnergyScint[b] is the Bethe-Bloch equation for energy deposit for a fully...
  12. S

    Double Logarithmic Scale: Find/Create Equation

    double log scale - please help I am trying to find/create the equation for a straight line on a double logarithmic scale graph - what is the format of the equation or how do I do this using data points from the graph.