1. INDICES AND LOGARITHMS
M24 IJSO 2008
INDICES AND LOGARITHMS

2. Content Laws of Indices Some Properties of Indices
Definition of Logarithms
Some Properties of Logarithms

3. M24 IJSO 2008
Laws of Indices

4. Some Properties of Indices

5. Proof of the properties
To prove:
Let
Then

6. Proof of the properties
To prove:
Let
Then

7. Proof of the properties
To prove:
Let
Then

8. Proof of the properties
To prove:

9. Definition of Logarithms
The log of x to the base a, written as logax is the value y such that ay = x, i.e.,
where a > 0 and a  1,
x > 0.

10. Particular Cases: and Common Logarithm (a = 10): or simply
Natural Logarithm (a = e = …):
or simply

11. Some Properties of Logarithms

12. Proof of the properties
To prove:
Let
and
Then
and

13. Proof of the properties
To prove:
Let
Then

14. Proof of the properties
To prove:

15. Proof of the properties
To prove:
Let
Then

16. Exercises
1. If , then what is ?
2. Compute