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Home » » Courses » Mathematics » Advanced Mathematics 3205 (delisted) » Unit 03 » Set 06 ILO 01 » Get Ready
Outcomes
In this lesson you will
- use graphing technology to approximate the solutions for complex exponential equations with graphs and "guess and check"
- recognize the need for a more reliable, accurate, and speedy method by which these types of equation can be solved.
- experiment with calculators and discover that the log button reverses the process of exponentiation.
By the end of this section students will be able to:
- demonstrate an understanding, algebraically and graphically, that the inverse of an exponential function is a logarithmic function
- demonstrate an understanding of the role of real numbers in exponential and logarithmic expressions and equations
- demonstrate an understanding of the relationships that exist between arithmetic operations and the operations used when solving equations
- apply real number exponents in expressions and equations
- model real-world phenomena using exponential functions
Introduction
Mathematical Modeling, Book 3 p.172 - 175
Going in Reverse is asking you to find the value of x for any given y value, with a large degree of accuracy, for exponential functions. When the bases or exponents can be made equal, then 
can be found for x with accuracy; however, it is not always possible to make the bases or the exponents the same. The solution to these situations leads you to logarithms, the graph of logarithms and the inverse function being the reflection in the line y = x.
This section should take 2 hours to complete.
Prerequisites
To be successful in this lesson, it would be helpful to know the following:
- solving exponential functions by converting to the same base
- determine the equation of exponential functions without using technology
- understand the meaning of zero and negative exponents