This behaviour is useful when we are looking at material properties. You can see from this scale that the higher values are ‘squashed’ towards the right-hand end and the lower values ‘spread out’ towards the left-hand end. On all the log graphs we use, we mark these intervals for you to make them easier to read without a calculator: Looking at the log scale between 1 and 10, we can calculate where all the intervals lie and plot them using the linear scale:Īnd we get a similar pattern between 10 and 100 (without showing the linear scale this time!): In maths terms this means that log(10 n)=n Use a calculator to check that you can go from a linear scale to a log scale and back again to the same point on the linear scale. So 2 on the log scale is at point log(2)=0.30 on the linear scale, 3 on the log scale is at log(3)=0.48 on the linear scale etc. You can find the log function on most calculators (note it is related to, but not the same as, the ln function). If the point on the log scale is p, then the equivalent point on the linear scale is log(p). The reverse of this procedure is going from the log scale to the linear scale. So point ‘X’ on the scale above is about 10 0.5 = 3.16 We can see that there is an easy relationship between the linear scale and the log scale - if the point on the linear scale is n then the equivalent point on the log scale is 10 n. Point 3 on the linear scale represents 1,000 (=10 3) on the log scale.Point 2 on the linear scale represents 100 (=10 2) on the log scale. ![]() Point 1 on the linear scale represents 10 (=10 1) on the log scale.So we need a scale which looks something like this: The decibel scale used for sound is another common example of a log scale. Logarithms are related to ‘times’ scales - for example in the Richter scale for earthquakes, an increase in 1 point on the scale corresponds to an increase of 10 times more energy released. We’re not going to go into the details of the maths of logarithms here, but will just give an idea of how and why we use them. Most of the material selection charts are plotted using logarithmic scales. Logarithms and log scales - an introduction Logarithms and log scales An introduction
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