PDF Log-Log Plots - University of Reading
Basic Mathematics
Log-Log Plots
R Horan & M Lavelle
The aim of this package is to provide a short self assessment programme for students who wish to acquire an understanding of log-log plots.
Copyright c 2003 rhoran@plymouth.ac.uk , mlavelle@plymouth.ac.uk
Last Revision Date: March 11, 2004
Version 1.0
Table of Contents
1. Introduction 2. Straight Lines from Curves 3. Fitting Data 4. Final Quiz
Solutions to Exercises Solutions to Quizzes
Section 1: Introduction
3
1. Introduction
Many quantities in science can be described by equations of the form, y = Axn. It is, though, not easy to distinguish between graphs of different power laws. Consider the data below:
yT
? ?
?
??
?
? ?
? ??
? ??
0
E
x
It is not easy to see that the red points lie on a quadratic (y = Ax2) and that the blue data are on a quartic (y = Ax4). It is, however, clear that the black points lie on a straight line! Results from the packages on Logarithms and Straight Lines enable us to recast the power curves as straight lines and so extract both n and A.
Section 1: Introduction
4
Example 1 Consider the equation y = xn. This is a power curve, but if we take the logarithm of each side we obtain:
log(y) = log(xn) = n log(x) since log(xn) = n log(x)
If Y = log(y) and X = log(x) then Y = nX. This shows the linear relationship. Plotting Y against X, i.e., log(y) against log(x), leads to a straight line as shown below.
log(y) T
1 n
0
E
log(x)
Here n is the slope of the line. Thus: from a log-log plot, we can directly read off the power, n.
Section 1: Introduction
5
Quiz Which of the following lines is a log-log plot of y = x2?
log(y) T
a
b
c?
?
?
?
4-
?
????d
2-
????1
?? 2
?
0
| 2
| 4
E
log(x)
(a) a (b) b (c) c (d) d Note that the scales on the two axes are not the same.
Section 2: Straight Lines from Curves
6
2. Straight Lines from Curves
Example 2 Consider the more general equation y = Axn. Again we take the logarithm of each side:
log(y) = log(Axn) = log(A) + log(xn)
log(y) = n log(x) + log(A)
since log(pq) = log(p) + log(q) since log(xn) = n log(x)
The function log(y) is a linear function of log(x) and its graph is a straight line with gradient n which intercepts the log(y) axis at log(A).
log(y) T
n 1 log(A)
0
E
log(x)
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.
Related download
- pdf byjeff rey heer michael bostock and vadim ogievetsky aur to
- pdf rolling 10year stock market return
- pdf wizard of wall street stock market project
- pdf navigate a year old bull market elevated geopolitical risk
- pdf nasdaq 100 index options
- pdf the callan periodic table of investment returns
- pdf southwest airlines co 2017 annual report to shareholders
- pdf log log plots university of reading
- pdf how to get data an introduction into quantmod
- pdf investor profile questionnaire
Related searches
- university of scranton log in
- university of minnesota college of education
- university of minnesota school of social work
- wharton school of the university of pennsylvania
- cost of university of scranton
- university of minnesota school of education
- differentiation of log log x
- derivative of log base 2 of x
- university of scranton cost of attendance
- university of south florida college of medicine
- university of phoenix ecampus log in
- university of minnesota masters of social work