The content is just an excerpt from the complete note for SS1 First Term Further Mathematics Lesson Note – Logarithms. Check below to download the complete DOCUMENT
WEEK TWO
LOGARITHMS
CONTENTS:
- Laws of Logarithms
- Change of Base of Logarithms.
- Use of Tables (greater than one and less than one).
- Logarithmic Equations.
SUB TOPIC: LAWS OF LOGARITHMS
In the last topic indices, we learnt that p = ax , e. g 1000 = 103 where 3 is called the index. We can express the same in logarithms form. Log a p = x or log 10 1000 = 3
What then is logarithms?
The logarithms of a number p to base a, where a is a positive number not equal to 1 is the index to which a must be raised to give p. This shows clearly that indices and logarithms are the same.
Log28 = 3 because 8 = 23
Log 39 = 2 because 9 = 32
Laws of Logarithms
- Loga(pq) = Logap + Logaq = Multiplication rule
e.g. if Log3(6×5) = Log36 + Log35
- Logaa = 1 e.g Log1010 = 1
- Loga(x/y) = Logax – Logay = Division Rule
- Loga(x)n = nLogax
- Loga1 = 0
- Loga(1/x) = Logax-1 = -1Logax
- If Logby = 1 then y = b
- If Logba = 1/Logab
- Logb = 1/nLogbx
- Logb Logyb = 1 for b and y positive and not equal to 1
- Log by = Log by / Log a
Examples:
- Simplify Log39 + Log321 – Log37
Solution:
Log39 + Log321 – Log37
= Log3(9×21÷7)
To gain full access to the note: DOWNLOAD FILE