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Why are important Semilog graphs? 
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#1
May912, 03:56 AM

P: 81

I've a graph similar to a 1/x^2 function, but it's only represents positive X values. The Y axis represents the duration in seconds, and X represents the number of objects. This graph shows that, as the number of objects grows, the time decreases.
If I want to represent this graph in a semilog graph, it will appear a straight line that increases monotonically. I would like to know how can I interpret this graph? Why semilog are important? Thanks, 


#2
May912, 04:44 AM

P: 4,573

Hey xeon123 and welcome to the forums.
According to this: http://en.wikipedia.org/wiki/Semilog_plot One axis is plotting on a logarithmic scale. The interpretation of this is that when something increases by 1 on a logscale then it is increasing a multiple of the base of the logarithm. A decrease means it is decreasing by the same rate (division). It's useful when you have to understand processes that change very rapidly either in an increasing way or in a decreasing way. Examples of where we use these kinds of processes include when we have to analyze things like decibel levels in sounds, earthquakes, and other phenomena when we have to quantify things in a sensical way that would otherwise be difficult using a nonlog based representation. The straightline should represent (if I have read the wiki page correctly) a standard exponential process, whereas graphs that are 'larger' will represent processes that increase more rapidly and the lower ones will represent ones that decrease a lot less rapidly. I would probably check for yourself by looking at the Wiki page to verify whether my interpretation was correct or not. 


#3
May912, 04:47 AM

P: 81

As I understand from another site (I couldn't understand properly the wiki), when we get a straight line in a loglog, or semilog graph, it proves that there's a relation between these 2 variables.



#4
May912, 05:02 AM

P: 4,573

Why are important Semilog graphs?



#5
May912, 05:25 AM

P: 4,573

Also I just realized I was wrong about the straightline: the straightline graph corresponds to y = ln(x). If you have things growing faster then they will be greater than this (it means that the derivative will be > 1/x). If it is increasing slower, then the curve will be below the straight line (derivative will be < 1/x).
Also you need to put the above in context when dealing with functions that are both smaller and larger that the normal logline. 


#6
May912, 05:44 AM

P: 81

Here's the site:
http://www.youtube.com/watch?v=fYHGr...feature=relmfu 


#7
May912, 08:47 AM

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If, on "loglog" graph paper, we have general straight line, we have ln(y)= Aln(x)+ B and, taking the exponential of both sides, [itex]e^{ln(y)}= e^{Aln(x)+ B}= e^{ln(x^A}e^B= (e^B)x^A[/itex] a polynomial or power function. If on "semlog" graph paper, we have a general straight line, we have y= Aln(x)+ B, a logarithmic relation. We could take the exponential of both sides and get [itex]e^y= e^Bx^A[/itex] which is equivalent to [itex]x= e^{B/A}e^{y/A}[/itex] so that x is an exponential function of y. 


#8
May912, 08:55 AM

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loglog graphs and semilog graphs were important tricks when it was impossible to generate sufficient values to portray a curved graph accurately.
Since a straight line is accurately drawn with only two pairs of values, loglogs and semilogs preserved maximum accuracy at minimal production cost. Today, we have the luxury of computers to make the arduous computing business for us, and these types of tricks will lose their utility. 


#9
May912, 09:13 AM

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#10
May912, 09:19 AM

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I have always wondered about the phrase "using technology". Paper and pencil are made using technology aren't they?



#11
May912, 09:47 AM

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But, that will be as true for other functional relationships than power laws and exponential relations as well... 


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