# Calculating the gradient of a logarithmic scale

1. Apr 12, 2012

### blizzard12345

1. The problem statement, all variables and given/known data

hi i have the folowing data i would like to plot in matlab

plotERRLW =

0.0466 0.0111 0.0074 0.0046
NX =

50 500 1000 2000
i am using a logarithmic graph to gain a straight line, if i wished to find the gradient of the line would i use the change in the original numbers or change in the numbers after i have taken a log of them?

(also if i have to take a log of them what base does loglog naturally plot)

i have tried a number of options already but can't seem to get the correct answer (i know it should be close to 2) thanks in advance

2. Relevant equations

i believe the data is of the form plotERRLW = NX^(alpha)

3. The attempt at a solution

so far i have been taking the log base 10 of the numbers in question and simply dividing the log of the error with the log of NX

A log plot of (x, y) is a plot of (x, log(y)). If it is a straight line, they you are saying that log(y)= ax+b so that $y= e^{ax+b}= e^be^{ax}=Ce^{ax}$, a general exponential function.
A "log-log" plot of (x, y) is a plot of (log(x), log(y)). If a log-log plot gives a straight line through the origin, then log(y)= a log(x) so that $y= x^a$.