LOGARITHMS & EXPONENTS & RADICALS
CHAPTER 1: EXPONENTS AND EXPONENTIAL FUNCTIONS
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1. EXPONENTS
A. INTEGER EXPONENTS
-Simplifying Rational Exponential Expression Vid 1 ,
-Adding Subtracting Exponential Expressions Vid 1 ,
-Adding Subtracting Exponential Expressions and Simplifying Vid 1 ,
-Substituting Exponential in Another Similar One Special Type Example Vid 1 ,
B. ROOTS AND RADICAL EXPRESSIONS
-Perfect square examples simplify + 4 operations Vid 1 ,
-Moving Exponential Expressions Out of the Square Root Vid 1 ,
-Adding and Subtracting Square Roots Vid 1 ,
-Multiplying Sum or Difference of Square Roots Vid 1 ,
-Rationalizing a Denominator Vid 1 ,
-Moving Exponential Expressions Out of the Radicals Vid 1 ,
-Working with Rational Exponents Vid 1 ,
-Multiplying Dividing Radicals by Rational Exponents Vid 1 ,
-Radical Equations
type 1 Vid 1 ,
C. RATIONAL EXPONENTS
D. REAL EXPONENTS
–The Number e
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2. EXPONENTIAL FUNCTIONS
A. BASIC CONCEPT
B. GRAPHS OF EXPONENTIAL FUNCTIONS
C. PROPERTIES OF EXPONENTIAL FUNCTIONS
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3. SIMPLE VARIATIONS OF EXPONENTIAL FUNCTIONS (OPTIONAL)
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4. APPLICATIONS OF EXPONENTIAL FUNCTIONS
A. EXPONENTIAL GROWTH
B. EXPONENTIAL DECAY
C. COMPOUND INTEREST
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CHAPTER 2: LOGARITHMS AND LOGARITHMIC FUNCTIONS
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1. LOGARITHMS
A. BASIC CONCEPT
B. TYPES OF LOGARITHM
1. Common Logarithms
2. Natural Logarithms
C. PROPERTIES OF LOGARITHMS
1. Changing the Base of a Logarithm
D. USING A TABLE OF LOGARITHMS
1. Parts of Logarithm
2. Using a Table of Logarithms
–Table of Logarithms
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2. LOGARITHMIC FUNCTIONS
A. BASIC CONCEPT
B. GRAPHS OF LOGARITHMIC FUNCTIONS
C. PROPERTIES OF LOGARITHMIC FUNCTIONS
1. Sign of a Logarithmic Function
2. Inverse of a Logarithmic Function
3. Monotone Property of Logarithmic Functions
–Logarithmic Spirals
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3. SIMPLE VARIATIONS OF LOGARITHMIC FUNCTIONS (OPTIONAL)
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4. APPLICATIONS OF LOGARITHMIC FUNCTIONS
A. THE RICHTER SCALE
B. THE pH SCALE
C. THE DECIBEL SCALE
–Estimating World Population
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CHAPTER 3: EXPONENTIAL AND LOGARITHMIC EQUATIONS & INEQUALITIES
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1. EXPONENTIAL EQUATIONS AND INEQUALITIES
A. EXPONENTIAL EQUATIONS
1. Equations of the Form af(x) = ag(x) Vid 1 ,
2. Equations of the Form af(x) = b
3. Equations of the Form af(x) = bg(x)
4. Working with Exponential Equations
5. Exponential Equations with a Unique Solution
6. Equations of the Form f(x)g(x) = f(x)h(x)
7. Exponential Equations with Parameters
B. EXPONENTIAL INEQUALITIES
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2. LOGARITHMIC EQUATIONS AND INEQUALITIES
A. LOGARITHMIC EQUATIONS
1. Equations of the Form logf(x) g(x) = b
2. Equations of the Form logf(x) g(x) = logf(x) h(x)
3. Working with Logarithmic Equations
4. Equations with Logarithms to Different Bases
5. Logarithmic Equations with a Unique Solution
6. Logarithmic Equations with Parameters
B. LOGARITHMIC INEQUALITIES
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3. SYSTEMS OF EQUATIONS AND INEQUALITIES
A. SYSTEMS OF EQUATIONS
B. SYSTEMS OF INEQUALITIES
–The Slide Rule
–What is a Logarithm?