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

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

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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

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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

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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.

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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:

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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:

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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

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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:

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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:

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