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  • MA120: Applied College Algebra
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  • Expanding and Condensing Logarithms
    COURSE INTRODUCTION
    Course Syllabus
    Unit 1: Equations and Inequalities
    Unit 1 Learning Outcomes
    1.1: Solving Linear and Rational Equations in One Variable
    Solving Linear Equations in One Variable
    Solving Linear Equations Practice
    Applications of Linear Equations
    Rational Equations
    Rational Equations Practice
    1.2 Quadratic, Radical, and Absolute Value Equations
    Complex Numbers
    Solve Quadratic Equations by Factoring
    Solving Quadratic Equations Practice
    Solve Quadratic Equations Using the Square Root Property
    Using the Quadratic Formula and the Discriminant
    Equations That Are Quadratic in Form
    Absolute Value Equations
    Absolute Value Equations Practice
    Radical Equations
    Radical Equations Practice
    1.3: Linear Inequalities
    Using Interval Notation and Properties of Inequalities
    Solve Simple and Compound Linear Inequalities
    Solve Simple and Compound Linear Inequalities Practice
    Absolute Value Inequalities
    Unit 1 Assessment
    Unit 1 Assessment
    Unit 2: Introduction to Functions
    Unit 2 Learning Outcomes
    2.1: Notation and Basic Functions
    The Rectangular Coordinate System and Graphs
    Defining and Writing Functions
    Properties of Functions and Basic Function Types
    2.2: Properties of Functions and Describing Function Behavior
    Finding the Domain of a Function Defined by an Equation
    Finding the Domain of a Function Define by an Equation Practice
    Finding Domain and Range from Graphs
    Finding Domain and Range from Graphs Practice
    Graphing Piecewise-Defined Functions
    Graphing Piecewise-Defined Functions Practice
    Calculate the Rate of Change of a Function
    Determine Where a Function Is Increasing, Decreasing, or Constant
    Increasing and Decreasing Functions Practice
    Unit 2 Assessment
    Unit 2 Assessment
    Unit 3: Algebraic Operations on Functions
    Unit 3 Learning Outcomes
    3.1: Composite Functions
    Creating and Evaluating Composite Functions
    Creating and Evaluating Composite Functions Practice
    Creating and Evaluating Composite Functions Practice II
    Finding the Domain of a Composite Function
    3.2: Transformations
    Graphing Functions Using Vertical and Horizontal Shifts
    Graphing Functions Using Vertical and Horizontal Shift Practice
    Graphing Functions Using Reflections
    Graphing Functions Using Reflections Practice
    Determining Whether a Function Is One-to-One
    Graphing Functions Using Stretches and Compressions
    Compressing and Stretching Graphs Practice
    Compressing and Stretching Graphs Horizontally Practice
    3.3: Inverse Functions
    Inverse Functions
    Inverse Functions Practice
    Unit 3 Assessment
    Unit 3 Assessment
    Unit 4: Linear Functions
    Unit 4 Learning Outcomes
    4.1: Linear Functions
    Representations of Linear Functions
    Interpreting Slope as a Rate of Change
    Interpreting Slope as a Rate of Change Practice
    Writing and Interpreting an Equation for a Linear Function
    Writing Equations of Lines Practice
    Graphing Lines Practice
    Parallel and Perpendicular Lines
    4.2: Modeling with Linear Functions
    Building Linear Models from Words
    Modeling a Set of Data with Linear Functions
    4.3: Fitting Linear Models to Data
    Finding the Line of Best Fit
    Graphing Calculator
    Unit 4 Assessment
    Unit 4 Assessment
    Unit 5: Polynomial Functions
    Unit 5 Learning Outcomes
    5.1: Quadratic Functions
    Understanding How the Graphs of Parabolas Are Related to Their Quadratic Functions
    Vertex and Zeros of a Quadratic Function Practice
    Finding the Domain and Range of a Quadratic Function
    Determining the Maximum and Minimum Values of Quadratic Functions
    5.2 Power and Polynomial Functions
    Power Functions
    Power Functions Practice
    Polynomial Functions
    5.3 Graphs of Polynomial Functions
    Identify the x-Intercepts of Polynomial Functions with Factorable Equations
    x-Intercepts of Polynomial Functions Practice
    Graphing Polynomial Functions
    Graphing Polynomial Functions Practice
    5.4 Dividing Polynomials
    Use Long Division to Divide Polynomials
    Long Division to Divide Polynomials Practice
    Use Synthetic Division to Divide Polynomials
    5.5 Finding Roots of Polynomial Functions
    Three Techniques for Evaluating and Finding Zeros of Polynomial Functions
    Using the Fundamental Theorem of Algebra and the Linear Factorization Theorem
    Unit 5 Assessment
    Unit 5 Assessment
    Unit 6: Rational Functions
    Unit 6 Learning Outcomes
    6.1: Characteristics of Rational Functions
    End Behavior and Local Behavior of Rational Functions
    End Behavior and Local Behavior of Rational Function Practice
    Domain and Range of Rational Functions
    Zeros of Rational Functions
    6.2: Finding Asymptotes of Rational Functions
    Vertical and Horizontal Asymptotes of Rational Functions
    Vertical and Horizontal Asymptotes of Rational Function Practice
    6.3: Graphs and Equations of Rational Functions
    Graphing Rational Functions
    Graphing Rational Functions Practice
    Unit 6 Assessment
    Unit 6 Assessment
    Unit 7: Exponential and Logarithmic Functions
    Unit 7 Learning Outcomes
    7.1: Introduction to Exponential Functions
    Properties of Exponential Functions
    Equations of Exponential Functions
    Financial Applications of Exponential Functions
    7.2: Graphs of Exponential Functions
    Characteristics of Graphs of Exponential Functions
    Transformations of Graphs of Exponential Functions
    Graphing Exponential Functions Practice
    7.3: Introduction to Logarithmic Functions
    Convert Between Logarithmic and Exponential
    Convert Between Logarithmic and Exponential Practice
    Common and Natural Logarithms
    7.4: Graphs of Logarithmic Functions
    Characteristics of Graphs of Logarithmic Functions
    Transformations of Graphs of Logarithmic Functions
    Graphing Logarithmic Functions Practice
    7.5: Properties of Logarithmic Functions
    Properties of Logarithms
    Expanding and Condensing Logarithms
    Logarithms Rules Practice
    Unit 7 Assessment
    Unit 7 Assessment
    Unit 8: Exponential and Logarithmic Equations
    Unit 8 Learning Outcomes
    8.1: Solving Exponential Equations
    Using Like Bases to Solve Exponential Equations
    Exponential Equations Practice
    Solving Exponential Equations Using Logarithms
    Exponential Equations Using Logarithms Practice
    8.2: Solving Logarithmic Equations
    Using the Definition of a Logarithm to Solve Logarithmic Equations
    Exponential Equations Practice II
    Solving Applied Problems Using Exponential and Logarithmic Equations
    Exponential Model Word Problems Practice
    8.3: Exponential and Logarithmic Models
    Models of Exponential Growth and Decay
    Half-Life Practice
    Using Logistic Growth Models
    8.4: Fitting Exponential and Logarithmic Models to Data
    Use Data to Build a Logarithmic Model
    Use Data to Build a Logistic Model
    Unit 8 Assessment
    Unit 8 Assessment
    Unit 9: Systems of Equations and Inequalities
    Unit 9 Learning Outcomes
    9.1: Systems of Linear Equations in Two Variables
    Introduction to Systems of Linear Equations
    Algebraic Methods for Solving Systems in Two Variables
    Substitution Method Practice
    Addition Method Practice
    Multiplication with Addition Method Practice
    Analyzing the Solution to a System in Two Variables
    An Application of Systems in Two Variables
    9.2: Systems of Linear Equations in Three Variables
    Solve Systems with Three Variables
    Classify Solutions to Systems with Three Variables
    Writing Systems of Equations as Matrices
    Equations as Matrices Practice
    9.3: Systems of Nonlinear Equations
    Algebraic Methods for Solving Systems of Nonlinear Equations
    Nonlinear Inequalities
    Unit 9 Assessment
    Unit 9 Assessment
    Unit 10: Introduction to Conic Sections
    Unit 10 Learning Outcomes
    10.1: Ellipses
    Writing Equations of Ellipses in Standard Form
    Equations of Ellipses Practice
    Graphing Ellipses
    Graphing Ellipses Practice
    10.2: Hyperbolas
    Writing Equations of Hyperbolas
    Writing Equations of Hyperbolas Practice
    Writing Equations of Hyperbolas Centered at the Origin Practice
    Graphing Hyperbolas
    10.3: Parabolas
    Parabolas Centered at the Origin
    Parabolas Not Centered at the Origin
    Graphing Parabolas Practice
    Unit 10 Assessment
    Unit 10 Assessment
    Unit 11: Introduction to Sequences and Series
    Unit 11 Learning Outcomes
    11.1: Sequences and Their Notations
    Sequences Defined by an Explicit Formula
    Sequences Defined by a Recursive Formula
    11.2: Arithmetic Sequences
    Write the Terms of an Arithmetic Sequence
    Use a Formula for an Arithmetic Sequence
    11.3: Geometric Sequences
    Write the Terms of a Geometric Sequence
    Use a Formula for a Geometric Sequence
    11.4: Arithmetic Series
    Use the Formula for an Arithmetic Series
    Summation Notation Practice
    Use the Formula for a Geometric Series
    Geometric Series Practice
    Unit 11 Assessment
    Unit 11 Assessment
    Study Guide
    MA120 Study Guide
    Certificate Final Exam
    MA120: Certificate Final Exam
    Saylor Direct Credit
    Course Feedback Survey
    Course Feedback Survey
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Table of contents

  • Expanding Logarithmic Expressions
  • Condensing Logarithmic Expressions
  • Using the Change-of-Base Formula for Logarithms
  • Logarithms Basics and properties
  1. MA120: Applied College Algebra
  2. Unit 7: Exponential and Logarithmic Functions
  3. 7.5: Properties of Logarithmic Functions
  4. Expanding and Condensing Logarithms

Expanding and Condensing Logarithms

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Logarithms Basics and properties


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Saylor Academy © 2010-2025 except as otherwise noted. Excluding course final exams, content authored by Saylor Academy is available under a Creative Commons Attribution 3.0 Unported license. Third-party materials are the copyright of their respective owners and shared under various licenses. See detailed licensing information. Saylor Academy®, Saylor.org®, and Harnessing Technology to Make Education Free® are trade names of the Constitution Foundation, a 501(c)(3) organization through which our educational activities are conducted.