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Logarithms (type 1)

Extracts from this document...

Introduction

  1. (a) Copy and complete the following table using your calculator. Give your answers to the correct four decimal places.

Log 2 + log 3

0.7782

Log 6

0.7782

Log 3 + log 7

1.3222

Log 21

1.3222

Log 4 + log 20

1.9031

Log 80

1.9031

Log 0.2 + log 11

0.3424

Log 2.2

0.3424

Log 0.3 + log 0.4

-0.9208

Log 0.12

-0.9208

(b) Do you see any pattern? Describe it in your own words.

When you multiply the two abscissas on the logs to find another abscissa of another log, you get the same result for the answer when you find the sum of the logs.

(c) Copy and complete the following table by choosing your own numbers. An example has been given

Log 5 + log 4

Log 20

1.3010

Log 6 + log 3

Log 18

1.2553

Log 7 + log 2

Log 14

1.1461

Log 8 + log 1

Log 8

0.9031

Log 9 + log 6

Log 54

1.7323

Log 10 + log 3

Log 30

1.4771

(d) Find a general pattern for log x + log y

...read more.

Middle

-0.3010

Log 0.5

-0.3010

(b) Do you see any pattern? Describe it in your own words.

When you divide the two abscissas on the logs that you are subtracting to find another abscissa of another log, you get the same result for the answer when you find the sum of the logs.

(c) Copy and complete the following table by choosing your own numbers. An example has been given

log 6 – log 2

Log 3

0.4771

Log 4 – log 2

Log 2

0.3010

Log 8 – log 3

Log 2.66

0.4248

Log 36 – Log 4

Log 9

0.9542

Log 18 – log 3

Log 6

0.7782

Log 15 – log 10

Log 1.5

0.1761

(d) Find a general pattern for log x - log y

Log x - log y = log (x/y)

(e) Can you suggest why this is true?

This rule is true because when you divide both of the abscissas they equal another abscissa and subtracting the two logs will equal the third log. Therefore the general pattern is true.

  1. (a) Copy and complete the following table using your calculator. Give your answers to the correct four decimal places.

4 log 2

1.2041

Log24

1.2041

5 log 6

3.8907

Log 65

3.8907

½ log 4

0.3010

Log 41/2

0.3010

Log 7

0.8450

Log 72/5

0.8450

-3 log 5

-2.0969

Log 5-3

-2.0969

...read more.

Conclusion

   = 0

  1. Where does the curve cut the x-axis?

The curve cuts the x-axis at 1

  1. Can x = 0? Can x < 0? Use your calculator to check your answers

x ≠ 0 - x cannot be equal to zero

x < 0 - x can be less than zero

  1. State the restricted domain of the function


x: x > -2

  1. Copy and complete the following table of values

x

0.000001

0.00001

0.0001

0.001

0.01

0.1

1

y = log x

-6

-5

-4

-3

-2

-1

0

  1. What can you say about the y-axis

It increases by 1 each time x is multiplied by 10.  From this, it is also an arithmetic sequence and would keep going up by one for infinity.

  1. Copy and complete the following table of values

X

1

2

3

4

5

6

7

8

9

10

y = log x

0

0.30

0.48

0.60

0.70

0.78

0.85

0.90

0.95

1

  1. Using a scale of 1cm to represent 1 unit on the x-axis and 2 cm to represent 1 unit on the y-axis, draw the curve y = log x

(Screen clipped for graphing package)

image00.png

...read more.

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