Name: 114 Exponent and Logarithm Problems – From the AwesomeMath Summer Program
Brand: XYZ Press
SKU: XYZ-1044
Price: 39.95 USD
Availability: InStock

This book covers the theoretical background of exponents and logarithms, as well as some of their important applications. Starting from the basics, the reader will gain familiarity with how the exponential and logarithmic functions work, and will then learn how to solve different problems with them. The authors give the readers the opportunity to test their understanding of the topics discussed by exposing them to 114 carefully chosen problems, whose full solutions can be found at the end of the book.

Authors

Titu Andreescu and Sean Elliott

Subjects

Algebra

Book Details

Hardcover: 150 pages
Publisher: XYZ Press (2016)
Language: English
ISBN-10: 0-9968745-6-9
ISBN-13: 978-0-9968745-6-4

This is a wonderful book and probably the only one in the mathematical literature that focuses

on presenting a coherent collection of methods and techniques for solving problems that

involve exponents and logarithms.

The general structure of the book is built on a few pillars : basics properties of exponents and

logarithms, algebraic techniques in exponents and logarithms, equations and systems of

equations with exponents and logarithms, inequalities involving exponents and logarithms,

exponents and logarithms in number theory and exponents and logarithms in calculus. In

conclusion, the book is not only very complete in terms of spheres involving exponents and

logarithms, but also coherent and well built in terms of sequencing the themes. Each of the

sections is presenting a very carefully selected collection of problems that range in difficulty

level from easy to hard.

The book is problem solving oriented, that means, the reader is confronted with many

exercises and questions to answer from the very beginning of a section. In fact, learning

throughout problem solving is probably one of the most efficient ways to improve someone’s

level of understanding Mathematics.

Moreover, the book presents a generous collection of proposed problems divided into two

categories : introductory and advanced problems. In addition, all proposed problems have

detailed solutions and, sometimes, more than one solution, to facilitate and to provide a

complete understanding of the concepts.

Finally, I strongly recommend this book to all students that are planning to write AMC 10-12,

AIME and USAMO tests, or any other type of mathematical competition. Also, the book

represents a treasure for teachers that are working with gifted students or for any coach that

guides a young mathlete to improve his scores in mathematical competitions.

Cerasela T. (Canada)

This book was very insightful as I begin learning about the connection between exponents and number theory. The problems allowed to me to experience exponents and logarithms in different forms. It was very engaging and was a great experience for me!

Yubo Z. (South Carolina)

Very interesting book, I hadn't seen any textbooks specifically focused on exponents/logarithms before. It begins with basic exponents/logs and their techniques, such as factoring and proving conditions. It gives you a lot of experience in how to solve such problems, as I personally found it pretty easy to make a silly mistake on these. This gave me more intuition to help me solve these equations/inequalities correctly. I really liked how it allowed me to apply past algebraic topics, such as AM-GM and Cauchy-Schwartz, on the problems here. There were also a few inequalities that I had to review, such as Chebyshev's. I am currently taking calculus and have not yet learned most topics, so I wasn't able to complete the last chapter of the book. However, I thoroughly enjoyed learning all these techniques and applying them to the problems at the end (which all have very detailed solutions).

Shirley T. (North Carolina)

This book is greatly organized. The first chapter covers basics and the rest are applications in different areas, from seemingly unrelated number theory to calculus. The example problems in the first chapter are good. The solutions are short and clever. For example, problem 1.9, it shows by converting from inverse to normal and from sum to multiplication, and then the problem can be simplified.

Wei H. (Washington)

114 Exponent and Logarithm Problems helped me get better at not only exponential equations, but in algebra (and in number theory). After learning the basics, you learn how to solve equations (and systems). You even learn how to solve inequalities involving them. Exponents and Logarithms appear often in Number Theory as well, and you learn tactics on how to solve them. Finally, there is a calculus portion that teaches you how to solve problems using basic calculus methods that isn't hard to learn. Overall, this book is very helpful, both in computational exams and olympiad, and I would continue reading Awesomemath publications.

Sriram K. (Kansas)