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Alternative Modality of Delivery for the Exponential and Logarithmic Functions

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Conference

2023 Fall Mid Atlantic Conference: Meeting our students where they are and getting them where they need to be

Location

Ewing, New Jersey

Publication Date

October 27, 2023

Start Date

October 27, 2023

End Date

January 10, 2024

Page Count

19

DOI

10.18260/1-2--45114

Permanent URL

https://peer.asee.org/45114

Download Count

67

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Paper Authors

biography

Daniel Blessner Pennsylvania State University, Wilkes-Barre Campus

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I'm a faculty member at the Penn State Wilkes Barre campus. I'm a civil and chemical engineer.

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Abstract

Alternative Modality of Delivery for the Exponential and Logarithmic Functions Making engineering education more understandable to students can be difficult due to the demanding mathematical requirements that the major requires. One specific area of great difficulty for students is understanding the exponential and logarithmic functions. One part of the problem is that the logarithmic functions are not presented with an actual formula. They are only known as two keys on a calculator “ln” and “log”. A second problem is that they are represented in math books by the symbol y = logbx. Note that this notation does not reinforce standard function notation y = f(x). Secondly it also does not reinforce the fact that a logarithm is an exponent from the exponential function. It could be written as x = logby. The role of the inverse function is also not reinforced with standard college algebra math book notation. The inverse functions role is to change an (x,y) coordinate from the exponential function y = b to the power of x to (y,x) via the logarithmic function. Logarithmic functions are classified as transcendental functions. A transcendental function cannot be written as a finite combination of algebraic expressions. This fact in most cases eliminates the equation from ever being seen by students. Students need an equation to gain a somewhat hands-on experience. This paper does not aim to eliminate the above-mentioned calculator keys from calculations but wishes to have students use the actual equation for a few examples. For simplicity only the first three terms from the selected natural logarithm function in its infinite formula will be used. These calculated values will then be compared to a value obtained with the “ln” calculator key. The second major problem is the notation used for these functions in college algebra math books. The familiar function notation that students are accustomed to seeing in previous algebra courses is lost when in the standard logarithmic function notation. Students don’t even realize that the familiar f in f(x) is being replaced by “ln” in y = lnx. Also note that the standard notation lnx does not include parentheses such as y = ln(x) which is part of the standard function notation. This paper is not written from a research perspective. There was no collected student data from surveys as to the effectiveness of this alternative approach. This paper is composed of the supplemental chapter needed for anyone interested in using this different teaching approach. This chapter will start with the introduction of the exponential functions and will show the transition to the inverse logarithmic functions. The inverse notation will be represented as x = f(y) = logb(y), not the traditional notation. In addition, only three variables will be used. These are x, y, and b. This supplemental chapter aims to reinforce the identity of the variables x, y, and b and not to interchange them.

Blessner, D. (2023, October), Alternative Modality of Delivery for the Exponential and Logarithmic Functions Paper presented at 2023 Fall Mid Atlantic Conference: Meeting our students where they are and getting them where they need to be, Ewing, New Jersey. 10.18260/1-2--45114

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