PreCalculus
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Change of Base
Posted on Mar 12, 2009
Topic: Logarithmic Functions
Discover the change of base rule for logarithms by examining the ratio of two logarithmic functions with different bases.
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Activity Key Steps:
In Problem 1, students compare the graphs of two logarithmic functions with different bases. They are to use the Trace feature to determine the values of the bases.
Students then use a function table to determine the constant factor of the two functions.
In Problem 2, students investigate the effect of the bases on the value of c by testing different values of the bases of logarithmic functions in the spreadsheet.
Then students find a formula to calculate c algebraically by rewriting the general logarithmic function and using the properties of logs. They can then use the formula for c, to change the base of a logarithmic function.
By the end of this activity, students are able to change the base of a logarithmic function, find the bases of logarithmic expressions, and find the constant factor.