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This topic covers: - Radicals & rational exponents - Graphs & end behavior of exponential functions - Manipulating exponential expressions using exponent properties - Exponential growth & decay - Modeling with exponential functions - Solving exponential equations - Logarithm properties - Solving logarithmic equations - Graphing logarithmic ...
In this section we examine exponential and logarithmic functions. We use the properties of these functions to solve equations involving exponential or logarithmic terms, and we study the meaning and importance of the number \(e\).
What are Exponential and Logarithmic Functions? Exponential Function Definition: An exponential function is a Mathematical function in the form y = f (x) = b x, where “x” is a variable and “b” is a constant which is called the base of the function such that b > 1.
This chapter reviews these laws before recalling exponential functions. Then it explores inverses of exponential functions, which are called logarithms. Recall that in an expression such as an in which a is raised to the power of n, the number a is called the base and n is the exponent.
In this section, we will discuss logarithmic functions and exponential functions. The exponent rules we learned last section also apply to the exponents we see in exponential functions, so here we will focus on the relationship between exponential and logarithmic functions.
We use the properties of these functions to solve equations involving exponential or logarithmic terms, and we study the meaning and importance of the number e. e. We also define hyperbolic and inverse hyperbolic functions, which involve combinations of exponential and logarithmic functions.
In this chapter, we will explore exponential functions, which can be used for, among other things, modeling growth patterns such as those found in bacteria. We will also investigate logarithmic functions, which are closely related to exponential functions.
Exponential and Logarithmic Functions. Learning Objectives. Identify the form of an exponential function. Explain the difference between the graphs of [latex] {x}^ {b} [/latex] and [latex] {b}^ {x}. [/latex] Recognize the significance of the number [latex]e. [/latex] Identify the form of a logarithmic function.
Identify the form of a logarithmic function. Explain the relationship between exponential and logarithmic functions. Describe how to calculate a logarithm to a different base. In this section we examine exponential and logarithmic functions.
Exploring with Technology. You can demonstrate the validity of Properties 5 and 6, which state that the exponential function f(x) ex and the logarithmic function g(x) ln. are inverses of each other as follows: aph ofSketch the graph of(f g)(x)(g f)(x) elnx, using.