Using Logarithms to Explore Power and Exponential Functions

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Power functions and exponential functions often describe the relationship between variables in physical phenomena. Power functions are equations of the form y = kxn (see fig. 1), where k is a nonzero real number and n is a nonzero real number not equal to 1. Exponential functions are equations of the form y = kbx (see fig. 2), where k is a nonzero real number and b is a positive real number. Students should be able visually to recognize these functions so that they can easily identify their appearance when experimental data are graphed. When physical phenomena appear to describe exponential and power functions, logarithms can be used to locate approximate functions that represent the phenomena.