# Practical Uses for Exponential and Logarithmic Functions

English: Logarithm function as the inverse of an exponential, shown on the same graph together with the 45° “mirror line”. (Photo credit: Wikipedia)

This week I am teaching my lessons on exponential and logarithmic functions.  These lessons are always interesting.  My students are not allowed to use calculators so they are “encouraged” to think about these functions and how they behave algebraically, which can be challenging.

I begin my lessons with a general exponential function f(x) = ax (for a > 0, a ≠ 1).  I discuss how the function behaves for a > 1 and 0 < a < 1.  I present the graphs of both and solicit engagement from my students while discussing the properties of the functions (and their corresponding graphs).

Next, I introduce logarithmic functions as the inverse function of exponential functions.  I use the properties of inverse functions to graph the general logarithmic function f(x) = loga(x).  Once the graph is complete, I discuss the properties of logarithmic functions with my students.

These concepts are usually difficult to grasp since most students are not used to thinking about math concepts in-depth.  This is the point in the semester where students begin to ask the big question: “How is this used in the real world?”  One student wanted to know if exponential and logarithmic functions are useful for real-world situations.  I told him they are and shared a few basic examples in class.  Of course the discussion motivated me to write this blog.

Here are a few practical uses for exponential and logarithmic functions:

Population Growth (the rate of growth of people, animals, etc.)

Exponential Decay (the rate of decay of organisms)

Compound Interest (the rate of growth of an interest bearing account)

Mortgage Payments (the rate of growth of interest on a mortgage account)

Earthquakes (their magnitude)

pH (a solutions level: acidic vs. basic/alkaline)

Decibel of Sound (the measure of sound levels)

There are so many practical uses for both functions, but I listed the most relevant uses for my students.  Most of my students should be able to relate to at least one item from the lists.  More information can be obtained by conducting a little research.

What are other practical uses for exponential and logarithmic functions?

Related Article:

QED Insight: A Practical Use for Logarithms

### Author: Math Education Concepts

I am a Co-founder of and Program Coordinator for Math Corps Philadelphia, a combined academic enrichment and mentoring program. I am the author of "Teacher Training Manual: Designed for Secondary Mathematics Teachers of African American Urban Students." I hold a Master of Education degree in Secondary Mathematics and have several years of experience teaching secondary and post-secondary mathematics.

### 4 thoughts on “Practical Uses for Exponential and Logarithmic Functions”

1. Let’s also include, for the young and young at heart, how these functions computer programs and programming.

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• Absolutely!!!

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2. Hey just wanted to give you a quick heads up. The words in your article seem to be running off the screen in Internet explorer. I’m not sure if this is a format issue or something to do with internet browser compatibility but I figured I’d post to let you know. The style and design look great though! Hope you get the issue fixed soon. Kudos

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• Thank you for visiting my site! Thank you for the heads up. It is a WordPress template. I will contact them and see what can be done.

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