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The logarithm segment of …

This programme covers algebraic expressions, powers, logarithms, multiplication, fractions, division, factorization, rules of logarithms, base manipulation, and solving logarithmic equations. Gain insights into the power of logarithms.

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The logarithm segment of …

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  1. The logarithm segment of …

  2. PROGRAMME F2 INTRODUCTION TO ALGEBRA

  3. Programme F2: Introduction to algebra Algebraic expressions Powers Logarithms Multiplication of algebraic expressions of a single variable Fractions Division of one expression by another Factorization of algebraic expressions

  4. Programme F2: Introduction to algebra Logarithms Powers Logarithms Rules of logarithms Base 10 and base e Change of base Logarithmic equations

  5. Programme F2: Introduction to algebra Logarithms Powers 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. Programme F2: Introduction to algebra Logarithms Logarithms 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. Programme F2: Introduction to algebra Logarithms Rules of logarithms The three basic rules are: These lead to:

  8. Programme F2: Introduction to algebra Logarithms Base 10 and base e 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. Programme F2: Introduction to algebra Logarithms Change of base The change of base formula that relates the logarithms of a number to two different bases is given as:

  10. Programme F2: Introduction to algebra Logarithms Logarithmic equations Logarithmic expressions and equations can be manipulated using the rules of logarithms. Example:

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