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====== Math 445 lecture 4: log-linear relations ======

===== 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)'' | $y = c \; 10^{mx}$ ^
| ''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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