How does the logarithmic scale work? Is there a method to place numbers?

Are the bases or powers placed on it? Is there an equation?How does the logarithmic scale work? Is there a method to place numbers?
plotting on a log scale may help you visualise/estimate a power / exponential relationship between variables





for a log[base10] axis, instead of marking 1,2,3,4,5...


0.01, 0.1,1,10,100 ... would be major gridlines


and you could mark subdivisions at


3/10 [log2] 5/10 [log3] 6/10 [log4] 7/10 [log5]


(where 3/10 is the ruler distance between gridlines and 2 is what you mark it etc)





for a log[base2] axis you will just have equally spaced gridlines marked 1/32 1/16 1/8 1/4 1/2 1 2 4 8 16 32 ...





to plot a value say 30 on a log[2] scale, you would go to the


16 - 32 box, and then estimate where to put 30. This becuase natural after a while becuase you only have to think 30/16 = 1 7/8 where the left hand gridline is 16 ~ 1 and the right hand gridline is 32~2





the end result is pretty much the same as plotting one set of values against the log of the other, but you save having to calculate and write down each of the logs.How does the logarithmic scale work? Is there a method to place numbers?
Basically the logarithms are a number system of it's own.


Back in the days without calculators they were good for using because they make difficult questions of multiplication, division and powers easier to calculate - often with the aid of log tables.





Always remember logs consists of three parts, (1) a base, (2) a power for the base and (3), this base with the power will have a value.





All logs values can be placed onto a graph. You can then read the values off the graph for a log to a certain power.





In equation form it would look like this:


b - base.


a - some power.


n - the value of the calculation.


b陋 = n


Now you can take the log of any number.


log b陋 = log n


a log b = log n


To get back to the number, take the anti-log.
Picture it like this; for base 10:





x -%26gt; log x


---------------


0.001 -%26gt; -3


0.01 -%26gt; -2


0.1 -%26gt; -1


1 -%26gt; 0


10 -%26gt; 1


100 -%26gt; 2


1000 -%26gt; 3





See the relationship?
A logarithmic scale works by taking the log (with respect to some base) of a set of raw data. The effect is that, when you graph the data, the distances on the number line become much smaller as the size of the numbers increase. For example, on the logarithmic scale for base 10, the distance between 10 and 100 is equal to the distance between 100 and 1000, which is equal to the distance between 1000 and 10,000.





Sometimes it is useful to use logarithmic units, which would relate to the original units by an equation of the form


Y = c log (X/X_0),


where c is a constant and X_0 is some (usually very small) reference quantity. Decibels (for loudness of sound) and Richter units (for earthquake magnitudes) are examples of logarithmic units.