Class notes

Exponents and Logarithms

0 purchase

Course
Mathematics I (MATSUR1)

Institution
Mangosuthu University Of Technology (MUT)

This section begins by reviewing the basic laws of indices and logarithms. Understanding of these laws is crucial in all the other areas you will encounter dealing with indices and logarithms, and that extends beyond this content area. Let’s begin by reviewing these laws from what you already ...

[Show more]

Preview 3 out of 20 pages

View example

Uploaded on September 2, 2021
Number of pages 20
Written in 2021/2022
Type Class notes
Professor(s) Mr. r sheshane
Contains All classes

apply the laws of indices
apply the laws of logarithms

Free

Also available in package deal from R300,00

Download Save

100% satisfaction guarantee
Immediately available after payment
Both online and in PDF
No strings attached

Document also available in package deal (1)

Mathematics 1

R 141,00 R 300,00 4 items

1. Class notes - Radian measure
2. Class notes - Conic sections
3. Class notes - Exponents and logarithms
4. Class notes - Exponential functions and equations
Show more

EXPONENTS AND LOGARITHMS
Tutorial Manual

MUT
Maths 1

,Exponential and Logarithmic Functions
Learning Outcomes
After completing this section, you should be able to
 Apply the laws of indices
 Apply the laws of logarithms

Introduction
This section begins by reviewing the basic laws of indices and logarithms.
Understanding of these laws is crucial in all the other areas you will encounter
dealing with indices and logarithms, and that extends beyond this content area.
Let’s begin by reviewing these laws from what you already know from high
school.

Laws of Indices
The following laws of indices are true for all the non-zero values of a, m and n:

1. 𝑎𝑚 × 𝑎𝑛 = 𝑎𝑚+𝑛 eg 𝑎3 × 𝑎9 = 𝑎3+9 = 𝑎12
2. 𝑎𝑚 ÷ 𝑎𝑛 = 𝑎𝑚−𝑛 eg 𝑎2 ÷ 𝑎−5 = 𝑎2−(−5) = 𝑎2+5 = 𝑎7
3. (𝑎𝑚 )𝑛 = 𝑎𝑚𝑛 eg (𝑎3 )2 = 𝑎3×2 = 𝑎6

The above 3 laws are the basic laws of indices and from these, we can generate
other important results:
4. 𝑎0 = 1
1
5. 𝑎−𝑚 = 𝑎𝑚
1
6. 𝑎𝑚 = 𝑚√𝑎

1

, Exponential Functions
By definition, an exponential function is one where the unknown variable (x) is
in the index. Examples of exponential functions are 2𝑥 , 3−𝑥 and 10𝑥+1 .
Mathematically we say an exponential function is any function given by 𝑦 = 𝑎 𝑥 ,
where 𝑎 > 0 and a ≠ 1.

The diagram below shows some members of the exponential family:

NOTE:
All the curves pass through the point (1;0). This is because when 𝑥 = 0, 𝑦 =
𝑎 𝑥 = 𝑎0 = 1. Also, the x-axis is an asymptote for all exponential functions; that
is, the exponential functions approach the x-axis but don’t get to ‘touch’ or ‘cross’
it. We saw 𝑎 𝑥 > 0 for all values of 𝑥.

Base 𝒆
In this course and in all engineering calculations, the most important exponential
is the exponential function given to base 𝑒. The number 𝑒 is an irrational number
with many important uses in engineering and finance. Please note e is not an
abbreviation for exponential, it is just a symbol. You will get to appreciate its
importance as we move along with the cause. The value of 𝑒 from your calculators
is 2.718… This base will take over from base 10 that you were used to in high
school. The function 𝑦 = 𝑒 𝑥 has the same shape as the exponential functions

2

The benefits of buying summaries with Stuvia:

Guaranteed quality through customer reviews

Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.

Quick and easy check-out

You can quickly pay through EFT, credit card or Stuvia-credit for the summaries. There is no membership needed.

Focus on what matters

Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!

Frequently asked questions

What do I get when I buy this document?

You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.

Satisfaction guarantee: how does it work?

Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.