UPDATE 2014-01-15: The attached .zip file now contains a Mathcad Prime 3.0 worksheet (.mcdx) and—for those of you who are still using earlier verisions of Mathcad—an Adobe Acrobat printout (.pdf) of the worksheet so can see how it is put together.
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Sometimes in life it is necessary to put a known value onto a logarithmic axis or to determine the value of a particular point on a logarithmic axis. Most often, these two tasks are performed in sequence, where a known value on the x-axis is projected up to a curve for which the equation is unknown and the projecting line is then reflected off the curve to cross the y-axis. The object, of course, is to determine the y value corresponding to x, and thus determine the complete x-y coordinate for the desired point on the curve.
Performing this procedure for two points on a straight curve on a log-log graph enables the user to determine the equation of the curve, which will be in the form y=a*x^b. This technique is used in a separate worksheet (Lusk_IDF Curves.mcdx) to determine the equations of Rainfall Intensity-Duration-Frequency Curves for use in hydrology calculations. For non-straight curves, it takes at least three points and a regression analysis to develop an equation that reasonably approximates the curve.
This worksheet uses logarithimic interpolation techniques to [a] put a known value onto a logarithmic axis (presumed to be the x-axis) and [2] determe the value of a particular point on a logarithmic axis (presumed to be the y-axis). The log-log graph below shows the procedure using corresponding values of x and y and defines the variables used herein.