Re: slope of a log log scale graph

"Nor Faizah " <a7khawarizmi@xxxxxxxxx> wrote in message <ftn1qi$3ea
$1@xxxxxxxxxxxxxxxxxx>...
Hello

I have plotted a log log scale graph and would like to find
the slope for a certain range on the graph. How do I find
it without calculating it manually (by taking two points on
the graph and apply the formula m=dy/dx) ?

Many thanks.
--------
When you say, "log-log", I believe you mean that originally there was a
function

y = f(x) ,

but instead of plotting y against x, you have plotted Y = log(y) against X =
log(x). If that is the case, the slope you see on the graph is not the same as
the slope of the original function. They are related according to the equation

dy/dx = (dy/dY)*(dY/dX)*(dX/dx)
= y*dY/dX*(1/x) = (y/x)*M

where M is a slope (derivative) of the curve as it appears on the log-log
graph. This means for example that if you have what appears on the log-log
graph to be a straight line with slope M, the derivative of the original curve,
dy/dx, is related to this M by the above (varying) relation, and that would not
be a straight line in x and y coordinates. On the other hand, if you use the
values listed on log-log axes in determining slope, then that is indeed the
derivative of the original function itself. It all depends on what data you are
making use of, x and y, or X and Y.

See the website:

<http://en.wikipedia.org/wiki/Logarithmic_scale#Log-log_plots>

for a discussion of this subject.

Roger Stafford

.

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