Exponential and Logarithmic functions

Chapter Summary:

This chapter defines and explores the exponential and logarithmic functions. We inspire exponential functions by their ‘similarity’ to the monomials and also their broad range of application. We introduce the logarithmic functions as inverse functions of the exponential functions and use our prior knowledge of inverse functions to explore such functions. In specific, we utilize this inverse relationship for the aim of solving exponential and logarithmic equations.

Exponential function f with the base a is f(x) = a^x, where a > 0, a ≠1, x ∈ R. Domain of f is R and the range is (0, ∞).

Logarithmic function g with the base a is inverse of the function

f(x) = a^x for a > 0, a ≠ 1. We can write g(x) = loga(x). That is, y = loga(x) if and only if y = x.

Domain of loga is (0, ∞), and the range is: (-∞, ∞).

Objectives:

• State the exponential and logarithmic functions.
• Examine the properties of the exponential and logarithmic functions.
• Introduce some of the applications of exponential and logarithmic functions.
• Solving exponential and the logarithmic equations.

Key topics included in this chapter are as follows:

a) Exponential Functions and Their Graphs
b) Logarithmic Functions and Their Graphs
c) Properties of Logarithms
d) Solving Exponential and Logarithmic Equations
e) Exponential and Logarithmic Models
f) Exploring Data: Nonlinear Models

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