Why do i get a stright line in both double and single logarithm paper ?

[mimi.janson]

Homework Statement

i have some data and i have to find out if they can be put in the function f(x)=a^x or f(x)=x^a
it is about how much time there goes before the population soemwhere grows or such.

Homework Equations

data: it is about the growth or a population in a villlage (way hard to explain)
time data: 15,59, 146,362, 571, 900
population; 72,69,67,65,64,63
addition: see the attachments. the red apaper is the doublelogarithm paper where i have put my data, and the grey is the single logarithm where i have put my data...but as you see the lines are both straight which is the problem

The Attempt at a Solution

then i have been thinking that u can actually just draw it and see if it makes a stright line in a double or single logarithm paper. and where it makes the stright line must be that funktion, but when i did draw it turned out to be stright in both the single logarithm paper and the double logarithm paper ...that is the reason why i need help...because i know it should only be stright in one of them yet it turned out to be in both

i hope that someone will help me

 

[mimi.janson]

why isn't anyone answering ? is my question to hard or am i explaining it wrong?
please give me an answer anyone

 

[Mark44]

It would be helpful if you included the data you are working with.

 

[mimi.janson]

It would be helpful if you included the data you are working with.

hello mark
i just added my data and two attachments on how the results look when i put them in both of the logaritm papers...only one line should be straight yet they both are and i can't figure out why...

 

[Ray Vickson]

hello mark
i just added my data and two attachments on how the results look when i put them in both of the logaritm papers...only one line should be straight yet they both are and i can't figure out why...

1) Your plots seem to show only 3 points, but you have 6 data points.
2) Change the scale on the second plot's x-axis, to spread it out better.
3) When I plot your data in Maple I get a straight line only for a log-log plot. The semi-log and direct plots are decidedly nonlinear.

RGV

 

[mimi.janson]

1) Your plots seem to show only 3 points, but you have 6 data points.
I suppose you are talking about the grey paper ? yes you can only see the three points on the computer, but i did put all six points on they just areant clear enough but the line goes right through them

2) Change the scale on the second plot's x-axis, to spread it out better.
Im sorry but i don't get the sentence here, could you please explain it differently? are you talking about changing data on the orange or grey one? and how can i just change the scale ?which one is the second plot ? i am sorry for my bad english

3) When I plot your data in Maple I get a straight line only for a log-log plot. The semi-log and direct plots are decidedly nonlinear.
so you say that the double logarithm paper is the only one linear (orange one i attached)? then does that mean that the one i did wrong was the grey one ? but i don't get how that one can be the wrong since it looked like the right one in the beginning.i mean when i first drawed i actually thought that it was the single logarithm that was the right...

 

[Ray Vickson]

1) Your plots seem to show only 3 points, but you have 6 data points.
I suppose you are talking about the grey paper ? yes you can only see the three points on the computer, but i did put all six points on they just areant clear enough but the line goes right through them

2) Change the scale on the second plot's x-axis, to spread it out better.
Im sorry but i don't get the sentence here, could you please explain it differently? are you talking about changing data on the orange or grey one? and how can i just change the scale ?which one is the second plot ? i am sorry for my bad english

3) When I plot your data in Maple I get a straight line only for a log-log plot. The semi-log and direct plots are decidedly nonlinear.
so you say that the double logarithm paper is the only one linear (orange one i attached)? then does that mean that the one i did wrong was the grey one ? but i don't get how that one can be the wrong since it looked like the right one in the beginning.i mean when i first drawed i actually thought that it was the single logarithm that was the right...

When I say "second one" I mean the orange plot. By 'spreading out', I mean re-scale time to something like 1.5, 5.9, 14.6, 36.2, 57.1, 90.0, so that your time values are not so squeezed together on the graph.

I suppose you did the gray (single log) plot incorrectly, but I cannot see how because the picture quality so poor. All I can tell you is what I got.

RGV

 

[mimi.janson]

When I say "second one" I mean the orange plot. By 'spreading out', I mean re-scale time to something like 1.5, 5.9, 14.6, 36.2, 57.1, 90.0, so that your time values are not so squeezed together on the graph.

I suppose you did the gray (single log) plot incorrectly, but I cannot see how because the picture quality so poor. All I can tell you is what I got.

RGV

firstly you said to change the scale on the second plot's x-axis, and now you say to change the time but i have the time on the y-axis ?it is like f(population)=... so my x is the population

Besides how can a person rescale the time on a log axis

and i did rescale on the single logarithm paper and for me that line seems really very straight...it's the one that was in poor quality before and now i have added a new version with this massage..so if you would take a look on it please

"When I plot your data in Maple I get a straight line only for a log-log plot. The semi-log and direct plots are decidedly nonlinear." when you wrote this i didn't get what log-log is ? do you mean you only get a straight line on the orange?

 

[Mark44]

Log-log paper has logarithmic scales on both axes. Semilog paper has a log scale only on the vertical axis.

This is the data that you eventually added to your first post.

time data: 15,59, 146,362, 571, 900
population; 72,69,67,65,64,63

I don't see how you got the plot that you show in post #8 from this data. The graph you show is a straight line (on log-log paper) with a positive slope, but your data shows that as time increases, the population is decreasing.

 

[Ray Vickson]

View attachment 40053

firstly you said to change the scale on the second plot's x-axis, and now you say to change the time but i have the time on the y-axis ?it is like f(population)=... so my x is the population

Besides how can a person rescale the time on a log axis

Its's easy: take logs of 1.5, 5.9, ... instead of 15, 59, ... which is exactly what I said already.

and i did rescale on the single logarithm paper and for me that line seems really very straight...it's the one that was in poor quality before and now i have added a new version with this massage..so if you would take a look on it please

"When I plot your data in Maple I get a straight line only for a log-log plot. The semi-log and direct plots are decidedly nonlinear." when you wrote this i didn't get what log-log is ? do you mean you only get a straight line on the orange?

Sorry: that may be a bit confusing; x and y axes are standard terminology. The x-axis is the horizontal one and the y-axis is the vertical. For example, I may plot volume versus pressure, with pressure (P) on the x-axis and volume (V) on the y-axis. You will see that type of description over and over and over again as you continue your studies.

Anyway, the plots I did were: semilog (plot of population vs. log(T) with log(T) on the x-axis), and log-log (plot of log(population) vs. log(T), with log(T) on the x-axis).

RGV

 

[mimi.janson]

Log-log paper has logarithmic scales on both axes. Semilog paper has a log scale only on the vertical axis.

This is the data that you eventually added to your first post.


I don't see how you got the plot that you show in post #8 from this data. The graph you show is a straight line (on log-log paper)the attachment i put in 8# wasn't log log paper but semilog...there is only a log scale on the vertical axis with a positive slopeit is not with a positive slope ...you see it like positive because therotated...look closely at the numbers ...by the way sorry couse i put it in rotated , but your data shows that as time increases, the population is decreasing.

And the thing about that attachment is that everyone here says that my data can only make a straight line on a log-log paper, but how come it also turns straight on a semilog when i put them...see the last attachment again
Besides i think i didn't really say it correctly what i am trying to do...but the teacher told that we can put the data on a normal paper, on a semi log and on a log-log and see which of the papers craetes a straight line...he said that we shouldn't take the log or anything of the numbers...just put them...and the time should be on the y-axis

 

[SammyS]

Anytime you make a plot with scaling set so that either the horizontal component of the data are very compressed or the vertical component of the data are very compressed, the result will be either a nearly horizontal line, or a nearly vertical line.

 

[Mark44]

And the thing about that attachment is that everyone here says that my data can only make a straight line on a log-log paper, but how come it also turns straight on a semilog when i put them...see the last attachment again

The image in post #8 is not good enough to be able to read the coordinates of the points. In any case, as I said before, you should not be getting a line with a positive slope.

time data: 15,59, 146,362, 571, 900
population; 72,69,67,65,64,63

The 15 in your time data should be paired with the 72 in your population data, and so on. Are you getting the order reversed?

 

[Ray Vickson]

View attachment 40053

Sorry: that may be a bit confusing; x and y axes are standard terminology. The x-axis is the horizontal one and the y-axis is the vertical. For example, I may plot volume versus pressure, with pressure (P) on the x-axis and volume (V) on the y-axis. You will see that type of description over and over and over again as you continue your studies.

Anyway, the plots I did were: semilog (plot of population vs. log(T) with log(T) on the x-axis), and log-log (plot of log(population) vs. log(T), with log(T) on the x-axis).

RGV

Sorry: my description is incorrect. The semilog plot has T on the x-axis and log(P) on the y-axis, while the log-log plot has log(T) on the x-axis and log(P) on the y-axis.

RGV

 

[mimi.janson]

The image in post #8 is not good enough to be able to read the coordinates of the points. In any case, as I said before, you should not be getting a line with a positive slope.

But it isn't positive slope ...I do not get a negative slope you just see it as positive because the picture on #8 is a bit upside down like 90 degreees to the left

The 15 in your time data should be paired with the 72 in your population data, and so on. Are you getting the order reversed?

what do you mean with getting it reversed? i did exactly as you are saying, but but it is going to kill me since iv'e used like three day and when i put my data in a exponential function they also are right and everything...the only problem is that my line in the log-log paper also is a straight line and i may not have two straight lines

 

[Mark44]

But it isn't positive slope ...I do not get a negative slope you just see it as positive because the picture on #8 is a bit upside down like 90 degreees to the left

Well, that explains why the slope appears to be positive. The image quality is so poor and the axes are not labelled, so I was not able to see this.