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\vskip -4.25in \vtop{\hsize=3.1in \noindent {\bf Problem statement} Some
loglog ``graph paper'' is shown to the right. The axes cross at
$(1,1)$, and spacing of the horizontal and vertical line segments on
the axes are both logarithmic so the distance between two labels on
each of the axes actually corresponds to the differences of the logs
of the labels. Use the ``graph paper'' carefully, since only some of
the crossings on the vertical axis are labeled.

\medskip

\noindent a) Consider the equation $y=1.5\,x^2$. Locate on the ``graph
paper'' those points corresponding to $x=1$, $x=2$, $x=3$, $x=4$,
$x=5$, and $x=6$ as well as you can. What seems to be the relationship
of these points?  What is the geometric slope of this relationship?

\medskip

\noindent b) Suppose that $x$ and $y$ are related by a power law, so
that $y=Ax^B$ where $A>0$. Verify that $\ln x$ and $\ln y$ are
related by an equation describing a straight line. What is the slope
of this line?

}


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