How does a logarithmic scale work
The ordinary linear scale we're familiar with starts from zero, and we can mark it by placing equal intervals to the right or left of it on a line. This uses addition or subtraction. A logarithmic scale works differently. At the beginning of such a scale is the number one.
To the right of one, at a distance of 1 cm, we place not 2, but 10. Another centimeter to the right will be 100. Another centimeter to the right—1,000, and so on. From this, it's clear that to find out how many intervals need to be laid out to the right, we need to determine the power to which 10 must be raised to get the desired number. And that's precisely what a logarithm is. The logarithm of number a to base b is the number to which base b must be raised to get a. I'll write it as log b(a).
For example, if we want to mark one million on the line, the number of intervals from the beginning of our scale will equal log 10(1,000,000), which is six. And how do we mark, say, 5? On a linear scale, this would be half an interval, but on a logarithmic scale, we need to lay out log 10(5). We take a calculator and find out that this equals 0.69897…, which is closer to the end of the interval. After several such calculations, it becomes clear that the interval is divided unevenly, unlike on a linear scale—numbers seem to cluster toward its end.
The logarithmic scale covers a larger range of numbers and finds application in a number of fields, for example, it's used to measure sound intensity or earthquake magnitude.