Logarithms (type 1)

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

Log x + log y = log (xy)

(e) Can you suggest why this is true?

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

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

(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

(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.

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

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

The number in front of the log is then used as the abscissa, raised to the power of the log, which then both give the same answer.

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

(d) Find a general pattern for n log x

n log x = log xn

(e) Can you suggest why this is true?

Say n = 4

Say x = 6

If you add log 6 together 4 times then you get the answer of 2.334. Which is the same as the answer for log 64

4. Consider the function y = log x

1. When x = 1, find the value of y

y = log 1

   = 0

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

The curve cuts the x-axis at 1

3. 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

4. State the restricted domain of the function

x: x > -2

5. Copy and complete the following table of values

6. 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.

7. Copy and complete the following table of values

8. 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)