Help with graphing formula on log scale

[somathinred]

Hi,

Part 1
How do I take two points and create a y(x) format formula for the line of those two points onto a graph that has a log y-axis and normal x axis?

Points would be (0, 5) and (3, 8)

Part 2
How do I find the point of intersection of two lines on a graph that has only y axis log and normal x axis?

This is a work related question, not homework for a class. Are there any websites you'd recommend that can perform the calculations for me?

 

[Ishuda]

Hi,

Part 1
How do I take two points and create a y(x) format formula for the line of those two points onto a graph that has a log y-axis and normal x axis?

Points would be (0, 5) and (3, 8)

Part 2
How do I find the point of intersection of two lines on a graph that has only y axis log and normal x axis?

This is a work related question, not homework for a class. Are there any websites you'd recommend that can perform the calculations for me?

You have to be careful if your are talking about how (semi) log graph paper is sometimes marked, for example
http://www.science-projects.com/SemiLogUse.htm
because the scale is sometimes marked (drawn) on a log scale and marked on a linear (regular) scale [see the red scale markings in the link]. So if you saw something on the graph marked like that at (0,5) it really would be x=0 and y=5. However, most of the time, the markings are as indicated in the link and you have to provide your own minimum starting value. For example, you might have data that is exponentially increasing and starts a little above 1000. The lower value [the red 1 marking at the link] would then be a 1000.

However, if you wanted a equally spaced scales graph where the vertical variable, f(x), was the log, then you would just have
f(x) = log(y(x))
and plot (x, f(x)).

As for graphically finding the point of intersection, it would be easiest to plot them on the same graph or at least the same type graph. If you have the formulas for the line and they are not to complicated, it may be easier to work out the intersection algebraically.

 

[somathinred]

You have to be careful if your are talking about how (semi) log graph paper is sometimes marked, for example
http://www.science-projects.com/SemiLogUse.htm
because the scale is sometimes marked (drawn) on a log scale and marked on a linear (regular) scale [see the red scale markings in the link]. So if you saw something on the graph marked like that at (0,5) it really would be x=0 and y=5. However, most of the time, the markings are as indicated in the link and you have to provide your own minimum starting value. For example, you might have data that is exponentially increasing and starts a little above 1000. The lower value [the red 1 marking at the link] would then be a 1000.

However, if you wanted a equally spaced scales graph where the vertical variable, f(x), was the log, then you would just have
f(x) = log(y(x))
and plot (x, f(x)).

As for graphically finding the point of intersection, it would be easiest to plot them on the same graph or at least the same type graph. If you have the formulas for the line and they are not to complicated, it may be easier to work out the intersection algebraically.

I appreciate the links. It's been quite a few years since I last was in an algebra class, so I've forgotten most of the basic calculation processes. I'm trying to figure out how to graph on a semi log for a work assignment that uses base 10. Given two sets of points, how do you proceed to construct a formula that you described above that I can plot? Some step by step instructions would be appreciated. If a website is available to do the calculations, then that'd be fine as well.

 

[Ishuda]

I appreciate the links. It's been quite a few years since I last was in an algebra class, so I've forgotten most of the basic calculation processes. I'm trying to figure out how to graph on a semi log for a work assignment that uses base 10. Given two sets of points, how do you proceed to construct a formula that you described above that I can plot? Some step by step instructions would be appreciated. If a website is available to do the calculations, then that'd be fine as well.

To plot on semi-log graph paper, look at the 3rd image of the graph paper at
http://www.science-projects.com/SemiLogUse.htm
with the red 1, 10, 100, 1000 marked on the side. The 2 between the 1 and 10 red markings is 2; the 2 between the 10 and 100 red markings is 20 (2 * 10), the 2 between the 100 and 1000 red markings is 200 (2*100). Similarly for the other numbers.

As an example: Suppose you had the set of (x,y) data
1, 2
2, 30
3, 450
You would plot a point at x = 1 and y = the 2 between the 1 and 10.
You would plot a point at x = 2 and y = the 3 between the 10 and 100, that is 30=3*10.
For the point at x = 3 and y = 450, note that the 5 between each consecutive pair of red scale marks is about 3/4 of the way from the smaller to the larger. So the 50 (=5*10) part of the 450 would be about 3/4 of the way between the 4 and 5 between the 100 and 1000 red markings.

Look at the examples offered on the page (y=a^N where a is 1.5, 2, and 3) for more examples.