Logarithmic and Exponential Equations

About Course

This course develops deep algebraic understanding of exponents, radicals, and logarithms, with a focused progression into solving exponential and logarithmic equations. Students will master the foundational rules, manipulate expressions fluently, and solve increasingly complex equations with precision. This course is ideal for Algebra 2 students preparing for upper-level math, standardized testing, or dual credit coursework.

Master the laws of exponents and apply them to simplify complex algebraic expressions
Understand and manipulate rational exponents and radicals with confidence
Convert seamlessly between radical and exponential forms to unlock multiple solution paths
Build fluency in simplifying and rationalizing radical expressions, including binomial denominators
Grasp logarithms as the inverse of exponents and develop number sense with log expressions
Apply core logarithmic properties to expand, condense, and simplify multi-part expressions
Solve exponential equations using matching bases and logarithmic methods
Tackle logarithmic equations step by step, avoiding common pitfalls like extraneous solutions
Combine radical, exponential, and logarithmic reasoning to solve layered equations
Strengthen your algebraic precision and deepen your readiness for Pre-Calculus and college-level math

Course Content

1. Exponent Rules and Rational Exponents
This topic builds fluency in exponent operations, from basic laws to rational exponents. Students will manipulate powers, apply algebraic rules, and connect exponents with radicals for future use in solving equations.

1.1 Laws of Exponents
1.2 Rational Exponents

2. Radical Expressions
Students will develop the ability to simplify radical expressions and rationalize denominators using algebraic strategies. This topic bridges radical notation and exponent rules in preparation for solving radical-based equations.

3. Introduction to Logarithms
This topic introduces logarithms as the inverse of exponentiation. Students will convert between forms, evaluate simple logs, and understand the foundational logic behind logarithmic operations.

4. Properties of Logarithms
Students will explore and apply the three main logarithmic properties (product, quotient, and power) and the change of base formula. These tools are essential for simplifying complex expressions and solving logarithmic equations later in the course.

5. Solving Exponential and Logarithmic Equations
This topic develops strategic approaches for solving exponential and logarithmic equations. Students will isolate terms, apply properties, and verify solutions — especially when extraneous roots may arise.

About Course

What Will You Learn?

Course Content

1. Exponent Rules and Rational Exponents
This topic builds fluency in exponent operations, from basic laws to rational exponents. Students will manipulate powers, apply algebraic rules, and connect exponents with radicals for future use in solving equations.

1.1 Laws of Exponents

1.2 Rational Exponents

2. Radical Expressions
Students will develop the ability to simplify radical expressions and rationalize denominators using algebraic strategies. This topic bridges radical notation and exponent rules in preparation for solving radical-based equations.

2.1 Simplifying Radicals

2.2 Rationalizing Denominators

3. Introduction to Logarithms
This topic introduces logarithms as the inverse of exponentiation. Students will convert between forms, evaluate simple logs, and understand the foundational logic behind logarithmic operations.

3.2 Evaluating and Simplifying Logs

3.1 Fundamental Concepts of Logarithms

4. Properties of Logarithms
Students will explore and apply the three main logarithmic properties (product, quotient, and power) and the change of base formula. These tools are essential for simplifying complex expressions and solving logarithmic equations later in the course.

4.1 Core Logarithmic Properties

4.2 Expanding and Condensing Logarithms

5. Solving Exponential and Logarithmic Equations
This topic develops strategic approaches for solving exponential and logarithmic equations. Students will isolate terms, apply properties, and verify solutions — especially when extraneous roots may arise.

5.1 Exponential Equations

5.2 Solving Logarithmic Equations

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Logarithmic and Exponential Equations

About Course

What Will You Learn?

Course Content

1. Exponent Rules and Rational Exponents This topic builds fluency in exponent operations, from basic laws to rational exponents. Students will manipulate powers, apply algebraic rules, and connect exponents with radicals for future use in solving equations.

1.1 Laws of Exponents

1.2 Rational Exponents

2. Radical Expressions Students will develop the ability to simplify radical expressions and rationalize denominators using algebraic strategies. This topic bridges radical notation and exponent rules in preparation for solving radical-based equations.

2.1 Simplifying Radicals

2.2 Rationalizing Denominators

3. Introduction to Logarithms This topic introduces logarithms as the inverse of exponentiation. Students will convert between forms, evaluate simple logs, and understand the foundational logic behind logarithmic operations.

3.2 Evaluating and Simplifying Logs

3.1 Fundamental Concepts of Logarithms

4. Properties of Logarithms Students will explore and apply the three main logarithmic properties (product, quotient, and power) and the change of base formula. These tools are essential for simplifying complex expressions and solving logarithmic equations later in the course.

4.1 Core Logarithmic Properties

4.2 Expanding and Condensing Logarithms

5. Solving Exponential and Logarithmic Equations This topic develops strategic approaches for solving exponential and logarithmic equations. Students will isolate terms, apply properties, and verify solutions — especially when extraneous roots may arise.

5.1 Exponential Equations

5.2 Solving Logarithmic Equations

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1. Exponent Rules and Rational Exponents
This topic builds fluency in exponent operations, from basic laws to rational exponents. Students will manipulate powers, apply algebraic rules, and connect exponents with radicals for future use in solving equations.

2. Radical Expressions
Students will develop the ability to simplify radical expressions and rationalize denominators using algebraic strategies. This topic bridges radical notation and exponent rules in preparation for solving radical-based equations.

3. Introduction to Logarithms
This topic introduces logarithms as the inverse of exponentiation. Students will convert between forms, evaluate simple logs, and understand the foundational logic behind logarithmic operations.

4. Properties of Logarithms
Students will explore and apply the three main logarithmic properties (product, quotient, and power) and the change of base formula. These tools are essential for simplifying complex expressions and solving logarithmic equations later in the course.

5. Solving Exponential and Logarithmic Equations
This topic develops strategic approaches for solving exponential and logarithmic equations. Students will isolate terms, apply properties, and verify solutions — especially when extraneous roots may arise.