Logarithm Complete Essay

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ADDITIONAL
MATHEMATICS
PROJECT WORK
1/2013

LOGARITHM

NAME :
CLASS : 5 GAMMA
I/C NO :
SCHOOL : SMK DARUL EHSAN
TEACHER : PUAN ROSMAZARAH BT SULONG

INDEX
NO
CONTENT
PAGE
1
Appreciation
3
2
Objective
4
3
Introduction
5
4
Part 1 Question
6-11
5
Conjecture
12
5
Part 2 Question
13-15
6
Part 3 Question
16-20
7
Further Exploration
21
8
Conclusion
22
9
Reflection
23

Appreciation Assalamualaikum.
As this Additional Mathematics Project Work for 2013 had been completed. I would like to show some appreciation to those people who have kindly to helped me to finish this project. First of all, I would like to thank my parent. Both my parent have supported all the materials to be used to finish this project. With their help and efforts, I have been able to finish this project right on time. Also, a special thanks to my Additional Mathematics subject teacher, Puan Rosmazarah bt Sulong. With lots of patience, she had thought me so much about the subject. She had also given many useful knowledge that have somehow motivated me. Lastly, I would also like to thank to all my group member and my classmates, especially Tan Siew Woon, Vicgneesh, Muhd Fazhan, Zaliq Syauqi, Ridhwan Rusydi Azri, Muhammad Adam, Muhammad Aizat Azri, and Ahmad Sobri for completing this project together. Teamwork made this project easier and is able to be finished at shorter time.

Objectives

The aims of carrying out this project work are:

to apply and adapt a variety of problem-solving strategies tosolve problems.

to improve thinking skills.

to promote effective mathematical communication.

to develop mathematical knowledge through problem solving in a way that increases students interest and confidence.

to use the language of mathematics to express mathematical ideas precisely.

to provide learning environment that stimulates and enhanceseffective learning.

to develop positive attitude towards mathematics

Introduction

One of the mathematical concepts which we must be familiar with is logarithms. Before the days of scientific calculators, logarithms were used to multiply or divide extreme numbers using mathematical tables. For these calculations, ten was the most common base to use. Logarithm to the base of ten is also called the common logarithm. Other bases such as two, five and eight can also be used. The ancient Babylonians had used bases up to 60.

Logarithms have many applications in various fields of studies. In the early 17th century it was rapidly adopted by navigators, scientists, engineers and astronomers to perform computations more easily.

PART 1
History of Logarithm

The logarithm of a number is the exponent to which another fixed value, the base, must be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the power 3: 1000 = 10 × 10 × 10 = 103. More generally, if x = by, then y is the logarithm of x to base b, and is written y = logb(x), so log10(1000) = 3. The Babylonians sometime in 2000–1600 BC may have invented the quarter square multiplication algorithm to multiply two numbers using only addition, subtraction and a table of squares. However it could not be used for division without an additional table of reciprocals. Large tables of quarter squares were used to simplify the accurate multiplication of large numbers from 1817 onwards until this was superseded by the use of computers.
Michael Stifel published Arithmetica integra in Nuremberg in 1544, which contains a table of integers and powers of 2 that has been considered an early version of a logarithmic table.
In the 16th and early 17th centuries an algorithm called prosthaphaeresis was used to approximate multiplication and division. This used the trigonometric identity

or similar to convert the multiplications to additions and table lookups. However logarithms are more straightforward and require less work. It
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