LOGARITHM

Introduction to Logarithm

In its simplest form, a logarithm answers the question:

How many of one number do we multiply to get another number?

Example 1: 

How many 2s do we multiply to get 8?

Answer 

2 x 2 x 2 = 8 

so we needed to multiply 3 of the 2s to get 8.

So the logarithm is 3. 

How to Write it:

We write "the number of 2s we need to multiply to get 8 is 3" as:

log₂(8) = 3

Example 2:

What is log₅(625) ... ?

We are asking "how many 5s need to be multiplied together to get 625?"

5 × 5 × 5 × 5 = 625, so we need 4 of the 5s

Answer: log₅(625) = 4

Example 3:

What is log₂(64) ... ?

We are asking "how many 2s need to be multiplied together to get 64?"

2 × 2 × 2 × 2 × 2 × 2 = 64, so we need 6 of the 2s

Answer: log₂(64) = 6

Exercise:

What is log3(27) ... ?

MEAN

What is Mean and how do we find it?

The mean is the average of the numbers.

It is easy to calculate: add up all the numbers, then divide by how many numbers there are.

In other words it is the sum divided by the count.


Example 1:

What is the Mean of these numbers?

6, 11, 7

• Add the numbers: 6 + 11 + 7 = 24
• Divide by how many numbers (there are 3 numbers): 24 / 3 = 8

The Mean is 8.

Example 2:

Look at these numbers: 

3, 7, 5, 13, 20, 23, 39, 23, 40, 23, 14, 12, 56, 23, 29

The sum of these numbers is 330

There are fifteen numbers.

The mean is equal to 330 / 15 = 22

The mean of the above numbers is 22.

Example 3:

Look at these numbers: 

5, 4, 3, 12, 2

The sum of these numbers is 26

There are five numbers.

The mean is equal to 26 / 5 = 5.5

The mean of the above numbers is 5.5.

Exercise:

Look at these numbers: 

12, 12, 14, 15, 23, 24, 25

Calculate the mean of the above numbers

INDICES

INDICES

Indices is the index of a number that says how many times to use the number in a multiplication. 

Rules of indices:

Example 1:

Work out 2^5 x 2^6 = 2^(5+6) = 2^11


Example 2:

Work out (4^5)^2 = 4^10



Example 3:

4/4 = 1 , 7/7 = 1 and 40/40 = 1

Exercise
a) Work out (4^2)^7
b) Work out 3^2 x 3^5