1. STROUD Worked examples and exercises are in the text The logarithm segment of …

2. STROUD Worked examples and exercises are in the text PROGRAMME F2 INTRODUCTION TO ALGEBRA

3. STROUD Worked examples and exercises are in the text Algebraic expressions Powers Logarithms Multiplication of algebraic expressions of a single variable Fractions Division of one expression by another Factorization of algebraic expressions Programme F2: Introduction to algebra

4. STROUD Worked examples and exercises are in the text Logarithms Powers Logarithms Rules of logarithms Base 10 and base e Change of base Logarithmic equations Programme F2: Introduction to algebra

5. STROUD Worked examples and exercises are in the text Logarithms Powers Programme F2: Introduction to algebra Any real number can be written as another number written raised to a power. For example: So that: Here the process of multiplication is replaced by the process of relating numbers to powers and then adding the powers – a simpler operation.

6. STROUD Worked examples and exercises are in the text Logarithms Programme F2: Introduction to algebra If a, b and c are three real numbers where: The power c is called the logarithm of the number a to the base b and is written:

7. STROUD Worked examples and exercises are in the text Logarithms Rules of logarithms Programme F2: Introduction to algebra The three basic rules are: These lead to:

8. STROUD Worked examples and exercises are in the text Logarithms Base 10 and base e Programme F2: Introduction to algebra On a calculator there are buttons that provide access to logarithms to two different bases, namely 10 and the exponential number e = 2.71828 … Logarithms to base 10 are called common logarithms and are written without indicating the base as log Logarithms to base e are called natural logarithms and are written as ln

9. STROUD Worked examples and exercises are in the text Logarithms Change of base Programme F2: Introduction to algebra The change of base formula that relates the logarithms of a number to two different bases is given as:

10. STROUD Worked examples and exercises are in the text Logarithms Logarithmic equations Programme F2: Introduction to algebra Logarithmic expressions and equations can be manipulated using the rules of logarithms. Example: