How Can Logarithmic Plots Test Exponential and Power Law Variations?

[ay2k]

[SOLVED] Logarithmic plots...

Homework Statement

use logarithmic plots to test exponential and power law variations

This statement appears in the Cambridge A'Level Syllabus

Can somebody please explain what does this statement require from the student?

Helpful links would be highly appreciated

Homework Equations

not relevant

The Attempt at a Solution

not relevant

 

[tiny-tim]

use logarithmic plots to test exponential and power law variations

Hi ay2k!

It just means do a graph with axes showing log(y) and x, or log(y) and log(x), instead of y and x.

The object is to get the students to choose a set of axes (a "plot") in which their experimental data should lie on a straight line!

 

[dynamicsolo]

There will, in fact, be two different versions you will need. The one tiny-tim describes will give a straight line for power-law functions, those which have the form y = A(x^n) ; such plots are (or at least used to be) called log-log plots. The other type uses log(y) vs. x , which gives a straight line for exponential functions, having the form y = C(e^n) ; these are called semi-log or log-linear plots.

 

[ay2k]

with exponential cases...we use ln right?not lg i suppose...

and how do we know that when to use ln or lg in exp case?

 

[ay2k]

with exponential cases...we use ln right?not lg i suppose...

and if so, how do we know that when to use ln or lg in exp case?

 

[tiny-tim]

with exponential cases...we use ln right?not lg i suppose...

and if so, how do we know that when to use ln or lg in exp case?

Hi ay2k!

You can use log or ln, it doesn't matter.

If you have log tables, use log.

If you have ln tables, use ln.

If you have both, use the base 10 one (I forget which way round it is! ), since that's easier!

 

[dynamicsolo]

In one sense, it doesn't matter. Whatever base you use for the logarithm, a general exponential function y = C·(a^n) will still give a straight line on a semi-log plot, since a logarithm to any base of a constant a will be a constant as well. People use ln or log_10 according to their taste or the standards of their field; mathematicians and physicists generally use natural logarithms, while most other scientists and engineers prefer common (base 10) logarithms.

 

[ay2k]

thankyou...my problem is solved...