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Logarithms

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Logarithms Concept Demonstrator

Dear TpT Friends - I am offering this software as a FREEBIE in the hopes that folks will download it, try it, and provide feedback on how to improve it.

The app requires Windows XP or later. It can also be run on Linux systems under Wine.

To use the app, download the product zip file and unzip it on your desktop. Then, open the unzipped folder and double click on

LogCalculator.exe

To remove the app from your computer, simply delete its containing folder.

The app is meant to provide support for concepts connected to logarithms. In addition to providing a basis for understanding the meaning of expressions like "log(28)", I hope the app will also give solid discovery-based insights into the Product Rule for logs
( log(ab) = log(a) + log(b) ), etc.

This particular version of the software covers logs of numbers greater than 1. If folks find the app useful, I will release a second version that covers logs of numbers between 0 and 1.

While your students are interacting with the log calculator, you may wish to emphasize that there are many interpretations of place-value expressions such as "2.35", and a logarithm is simply an alternative interpretation. For example, the conventional place-value interpretation of "2.35" decodes the numeral in terms of addition: "2 of these plus 3 of those plus 5 of those". On the other hand, the logarithmic place-value interpretation of "2.35" decodes the numeral in terms of multiplication: "2 of these times 3 of those times 5 of those". There's more than one way to skin a cat, and there's more than one way to write a recipe for building a set. It's actually pretty simple!

NOTE: Some students will ask, "Why are we using these particular factors?" A great question! Please have them place 10 instances of a given factor onto the workbench and inspect the result. For any of the factors, the product is always - to within the rounding error - the next-larger factor! This is an extremely important characteristic. If the result was less than the next-larger factor, then there would exist values in between these two quantities that you simply could not represent accurately using a logarithm. On the other hand, if the result was greater than the next-larger factor, then there would be multiple ways to express the same value. In order for the logarithm "scheme" to be complete without also being redundant, the factors must have this relationship to one another.
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