• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

Investigating Logarithms

Extracts from this document...

Introduction

Jeremiah Joseph

Investigating Logarithms

log2 + log3

0.7782

log6

0.7782

log3 + log7

1.322

log21

1.322

log4  + log 20

1.903

log80

1.903

log0.2 + log11

0.3424

log2.2

0.3424

log0.3 + log 0.4

-0.9208

log0.12

-0.9208

This table to the left clearly shows that the log of 2 numbers added together will equal the log of the number multiplied. The table below clearly shows that log (χ) + log (y) will equal log (χy). Let log x = a, let log y = b. Therefore 10a = x and 10b = y, these two equations can then be simplified to 10(a+b) =x*y. it is then possible to convert this back to log (xy) = a + b.

log5 + log4

log20

1.301

log3 + log2

log6

0.7782

log4 + log8

log32

1.505

log6 + log3

log18

1.255

log3 + log26

log78

1.892

log7 + log4

log28

1.447

log12 – log3

0.6021

log4

0.6021

log50 – log2

1.398

log25

1.398

log7 – log5

0.1461

log1.4

0.1461

log3 – log4

-0.1249

log0.75

-0.1249

log20 – log40

-0.3010

log0.5

-0.3010

...read more.

Middle

image00.png) – log (image03.pngimage03.png) will equal log (image04.pngimage04.png). Let log x = a, let log y = b. Therefore 10a = x and 10b = y, these two equations can be converted into 10(a – b) = x/y. Finally, this equation can then be converted back into log x – log y = log (x/y).

log6 – log2

log3

0.4771

log18 – log3

log6

0.7782

log 16 – log 2

log8

0.9031

log50 – log5

log10

1

log25 – log5

log5

0.6989

log32 – log8

log4

0.6021

4 log2

1.204

log24

1.204

5 log6

3.891

log65

3.891

½ log4

0.3011

log41/2

0.3011

...read more.

Conclusion


Let’s investigate the function y = log x

When x = 1, y = log1, therefore, y = 0

Therefore when y = 0, x will equal 1. On a graph this would mean that the curve would cut the x axis at 1. In this function x cannot equal zero or less than zero, this means that the restricted domain of the function will be image01.pngimage01.png{x: x>1}.

x

0.000001

0.00001

0.0001

0.001

0.01

0.1

1

y = log x

-6

-5

-4

-3

-2

-1

0

The table above displays that as x is multiplied by ten, the y value increases by 1.

x

1

2

3

4

5

6

7

8

9

10

y = log x

0

0.3010

0.4771

0.6021

0.6989

0.7782

0.8451

0.9010

0.9542

1

The graph below demonstrates the curve of the function y = log x

image02.png

Jeremiah Joseph        Maths Internal Assessment  Mr. Filander

...read more.

This student written piece of work is one of many that can be found in our International Baccalaureate Maths section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related International Baccalaureate Maths essays

  1. Logarithms. In this investigation, the use of the properties of ...

    First Sequence (4)(8) = 32 Second Sequence (7)(49) = 343 Third Sequence (1/5)(1/125) = 1/625 Fourth Sequence (8)(2) = 16 Values found using the base numbers of the first and second logarithms. Different values can be used for the nth terms in a sequence.

  2. Mathematics Higher Level Internal Assessment Investigating the Sin Curve

    In general it is observed that in the equation the period of the curve is given by . By changing the value of you can change the period of the graph. When you increase the the period of the graph decreases and when you decrease the the period of the graph increases.

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work