IB Class 10 Mathematics – Group 5, Algebra | 12. Introduction to Logarithms by Abraham | Learn Smarter
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12. Introduction to Logarithms

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Sections

  • 1

    Definition Of A Logarithm

    This section introduces the concept of logarithms as the inverse operation of exponentiation, providing definitions and foundational relationships.

    Learning Practice

  • 2

    Converting Between Forms

    This section covers the process of converting between exponential and logarithmic forms, providing foundational knowledge for understanding logarithms.

    Learning Practice

  • 2.1

    Exponential To Logarithmic

    This section explores the conversion between exponential and logarithmic forms, focusing on the definitions and relationships between the two.

    Learning Practice

  • 2.2

    Logarithmic To Exponential

    This section explains the relationship between logarithmic and exponential forms, providing various examples and laws of logarithms essential in solving equations.

    Learning Practice

  • 3

    Laws Of Logarithms

    This section covers the fundamental laws of logarithms, essential for simplifying expressions involving logarithmic functions.

    Learning Practice

  • 3.1

    Product Rule

    The Product Rule in logarithms states that the logarithm of a product is the sum of the logarithms of the factors.

    Learning Practice

  • 3.2

    Quotient Rule

    The Quotient Rule of logarithms enables the simplification of logarithmic expressions involving division.

    Learning Practice

  • 3.3

    Power Rule

    The Power Rule of logarithms simplifies the evaluation of logarithmic expressions involving exponents.

    Learning Practice

  • 3.4

    Change Of Base Formula

    The Change of Base Formula is a useful tool for converting logarithms from one base to another and facilitates the use of calculators to evaluate logarithmic expressions.

    Learning Practice

  • 4

    Common And Natural Logarithms

    This section introduces common and natural logarithms, explaining their definitions and notation.

    Learning Practice

  • 4.1

    Common Logarithms

    This section introduces common logarithms and their relationship to exponents and logarithmic equations.

    Learning Practice

  • 4.2

    Natural Logarithms

    This section introduces natural logarithms and their significance in mathematics, particularly emphasizing the relationship between natural logarithms and the constant e.

    Learning Practice

  • 5

    Evaluating Logarithms

    This section covers how to evaluate logarithmic expressions, both with and without the use of a calculator.

    Learning Practice

  • 5.1

    Without Calculator

    This section introduces logarithmic expressions and their evaluation without calculators, utilizing fundamental properties of logarithms and exponentials.

    Learning Practice

  • 5.2

    With Calculator

    This section teaches students how to evaluate logarithms using a calculator, specifically focusing on common logarithms (base 10) and natural logarithms (base e).

    Learning Practice

  • 6

    Solving Logarithmic Equations

    This section focuses on solving logarithmic equations by converting to exponential form and applying the laws of logarithms.

    Learning Practice

  • 6.1

    Example 1

    Learning

  • 6.2

    Example 2

    This section explores logarithmic equations and provides instructional examples for solving them.

    Learning Practice

  • 6.3

    Example 3

    This section focuses on solving logarithmic equations through examples.

    Learning Practice

  • 7

    Practice Exercises

    This section provides practice exercises to convert between logarithmic and exponential forms, simplify logarithmic expressions, and solve logarithmic equations.

    Learning Practice

  • 7.1

    Convert To Logarithmic Form

    This section teaches students how to convert numbers between exponential and logarithmic forms, highlighting the relationship between the two.

    Learning Practice

  • 7.2

    Convert To Exponential Form

    This section focuses on converting logarithmic expressions into exponential form, emphasizing the relationship between the two concepts.

    Learning Practice

  • 7.3

    Simplify

    This section breaks down the process of simplifying logarithmic expressions using logarithmic laws.

    Learning Practice

  • 7.4

    Solve

    The section focuses on solving logarithmic equations by converting from logarithmic to exponential form and applying the laws of logarithms.

    Learning Practice

  • 8

    Summary

    This section summarizes the key concepts of logarithms, highlighting their definitions, properties, and applications.

    Learning Practice

References

10 IB algebra ch12.pdf

Class Notes

Memorization

Revision Tests