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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 1.301 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

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 0.301 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 0.301 Log 41/2 0.301 Log 7 0.845 Log 72/5 0.845 -3 log 5 -2.0969 Log 5-3 -2.0969

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 1e-06 1e-05 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 0.3 0.48 0.6 0.7 0.78 0.85 0.9 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) This student written piece of work is one of many that can be found in our AS and A Level Core & Pure Mathematics section.

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