Exercises of Logarithms and Exponentials E-Book

Simone Malacrida

• Herausgeber: Simone Malacrida
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Veröffentlichungsjahr: 2022

Beschreibung

In this book, exercises are carried out regarding the following mathematical topics:
logarithmic functions and properties
exponential functions and properties
logarithmic and exponential equations and inequalities.
Initial theoretical hints are also presented to make the performance of the exercises understood.

Leseprobe

Table of Contents

“Exercises of Logarithms and Exponentials”

INTRODUCTION

THEORETICAL OUTLINE

EXERCISES

“Exercises of Logarithms and Exponentials”

SIMONE MALACRIDA

In this book, exercises are carried out regarding the following mathematical topics:

logarithmic functions and properties

exponential functions and properties

logarithmic and exponential equations and inequalities.

Initial theoretical hints are also presented to make the performance of the exercises understood.

Simone Malacrida (1977)

Engineer and writer, has worked on research, finance, energy policy and industrial plants.

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ANALYTICAL INDEX

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INTRODUCTION

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I – THEORETICAL OUTLINE

Exponential functions

Logarithmic functions

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II – EXERCISES

Exercise 1

Exercise 2

Exercise 3

Exercise 4

Exercise 5

Exercise 6

Exercise 7

Exercise 8

Exercise 9

Exercise 10

Exercise 11

Exercise 12

Exercise 13

Exercise 14

Exercise 15

Exercise 16

Exercise 17

Exercise 18

Exercise 19

Exercise 20

Exercise 21

Exercise 22

INTRODUCTION

In this exercise book, some examples of calculations relating to exponential and logarithmic functions are carried out.

These functions make it possible to complete the study of transcendent functions and form the necessary prerequisite for tackling the conceptual leap of mathematical analysis.

In order to understand in more detail what is presented in the resolution of the exercises, the theoretical reference context is recalled in the first chapter.

What is exposed in this workbook is generally addressed during the fourth year of scientific high schools.

I

THEORETICAL OUTLINE

Exponential functions

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Exponential functions are those functions that generalize exponentiation in which it is not the exponent that is numerical, but the base.

The general form of an exponential function is given by:

If a equals zero, the function is always zero.

If a equals one the function is always one.

For x=0 the exponential functions are all equal to one regardless of the value of the base.

Of particular importance are the exponential functions with a base equal to ten or equal to the number and of Nepero, whose value is given by:

with very large n.

This value corresponds to an irrational number.

The exponential function having a base equal to this number (called natural base) is indicated as follows: