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Log-linear relations

Logarithmic plots are useful when the data you're plotting varies over many orders of magnitude. Logarithmic plots can also highlight certain functional relationships

plot command	functional relationship
`plot(x,y)`	$y = mx + b$
`semilogy(x,y)`	$y = c \: 10^{mx}$ or $y = c \: e^{ax}$
`semilogx(x,y)`	$y = m \log x + b$
`loglog(x,y)`	$y = c \: x^m$

In lecture I will show (1) why each of these functional relationships appears as a straight line in the corresponding plot command and (2) how to estimate the values of the constants from a graph, in order to estimate $y(x)$ as an explicit function, given a few data points.

You can derive these formulae from the log-linear relations instead of memorizing them. For example, you can derive $y = c \; 10^{mx}$ by exponentiating both sides of $\log y = m x + b$ .

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