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# Exponentials and logarithms. Lecture 2.1

## 1. Lecture 2.1 Exponentials and Logarithms

Foundation Year ProgramNUFYP Mathematics

Lecture 2.1

Exponentials and Logarithms

Lecture slides prepared by:

Robert Farrell

Gonçalo Pinto

Rustem Iskakov

2019-2020

## 2. Lecture Outline

Foundation Year ProgramLecture Outline

Exponent

Exponential function

Graphs of exponential functions

Logarithm

Graphs of logarithmic functions

Laws of logarithms

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## 3. Introduction

Foundation Year ProgramIntroduction

What is exponent?

What is the basic idea of exponentiation?

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## 4. Introduction

Foundation Year ProgramIntroduction

What is exponent? Exponent is an index or power.

What is the basic idea of exponentiation?

2019-2020

## 5. Introduction

Foundation Year ProgramIntroduction

What is the basic idea of exponentiation?

5

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## 6. Introduction

Foundation Year ProgramIntroduction

What is the basic idea of exponentiation?

Repeated

addition

Repeated

multiplication

6

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## 7.

Foundation Year ProgramExponential function

An exponential function has the form

Exponent, index, power

(variable)

f(x) = ax

• where a is constant

• a ≠1, a > 0

Examples:

base

f (x) = 2x , f(x) = 3x , f(x) = ex

7

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## 8.

Foundation Year Program2.1.1 Sketch the graph of Exponential function

Let us see some graphs of exponential functions with

different bases on the same axes:

The larger the base ⇾ steeper the graph

y-intercept (0; 1)

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## 9.

Foundation Year ProgramAn exponential function has the form

Exponent, index, power

(variable)

Why a ≠1?

f(x) = ax

• where a is constant

• a ≠1, a > 0

base

Examples: