Exponential Equations: Matching Bases to Solve

Algebra 2 Grades High School 1:53 Video
Print Lesson Plan Watch Video

Lesson Description

Learn to solve exponential equations by manipulating bases to be equal. This lesson covers rewriting bases, applying exponent rules, and solving the resulting equations.

Video Resource

Solve an Exponential Equation by Getting Bases to be Equal

Mario's Math Tutoring

Duration: 1:53
Watch on YouTube

Key Concepts

  • Exponential Equations
  • Properties of Exponents
  • Rewriting Bases

Learning Objectives

  • Students will be able to rewrite exponential equations with different bases to have the same base.
  • Students will be able to apply properties of exponents to simplify exponential expressions.
  • Students will be able to solve exponential equations by equating exponents after achieving the same base.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the definition of an exponential equation and the goal of solving for the variable in the exponent. Briefly discuss the properties of exponents that will be used in the lesson.
  • Video Demonstration (10 mins)
    Play the Mario's Math Tutoring video 'Solve an Exponential Equation by Getting Bases to be Equal.' Encourage students to take notes on the example problem presented in the video.
  • Guided Practice (15 mins)
    Work through a similar example problem on the board, guiding students through each step. Emphasize the importance of identifying common bases and correctly applying the power of a power rule. Address any questions or misconceptions that arise.
  • Independent Practice (15 mins)
    Provide students with several exponential equations to solve on their own. Circulate the classroom to provide assistance as needed.
  • Wrap-up and Extension (5 mins)
    Summarize the key steps for solving exponential equations by equating bases. Briefly introduce the concept of using logarithms to solve exponential equations when bases cannot be easily equated (as mentioned in the video description), and refer them to the linked video for further exploration.

Interactive Exercises

  • Base Transformation Challenge
    Provide students with a set of numbers and challenge them to express each number as a power of a specific base (e.g., express 8, 16, 32, and 64 as powers of 2).
  • Equation Matching Game
    Create cards with exponential equations and cards with their corresponding solutions. Have students match the equations to their solutions.

Discussion Questions

  • Why is it important to have the same base on both sides of the equation before equating exponents?
  • What strategies can you use to identify a common base when given an exponential equation?
  • When would you need to use logarithms instead of this method?

Skills Developed

  • Problem-solving
  • Analytical thinking
  • Application of exponent rules

Multiple Choice Questions

Question 1:

What is the first step in solving an exponential equation by equating bases?

Correct Answer: Rewrite the bases to be the same

Question 2:

Which property of exponents is used when simplifying (a^m)^n?

Correct Answer: Power of a power

Question 3:

Solve for x: 2^x = 8

Correct Answer: x = 3

Question 4:

Solve for x: 3^(x+1) = 9

Correct Answer: x = 1

Question 5:

Solve for x: 5^(2x) = 25

Correct Answer: x = 1

Question 6:

Simplify: (4^2)^(1/2)

Correct Answer: 4

Question 7:

Rewrite 1/9 as a power of 3

Correct Answer: 3^-2

Question 8:

What is the common base for solving 4^x = 8?

Correct Answer: 2

Question 9:

If 2^(x+1) = 4^(x-1), what is x?

Correct Answer: 3

Question 10:

When is it impossible to solve using the method of equal bases?

Correct Answer: When the bases cannot be written in terms of a common base

Fill in the Blank Questions

Question 1:

An equation where the variable is in the exponent is called an _______ equation.

Correct Answer: exponential

Question 2:

When raising a power to another power, you _______ the exponents.

Correct Answer: multiply

Question 3:

If a^x = a^y, then x must equal _______.

Correct Answer: y

Question 4:

To solve 4^x = 2^(x+1), rewrite 4 as 2 to the power of _______.

Correct Answer: 2

Question 5:

3^(x-1) = 1 can be solved by rewriting 1 as 3 to the power of _______.

Correct Answer: 0

Question 6:

The expression 5^(-2) is equal to 1 over _______.

Correct Answer: 25

Question 7:

The first step to solving 9^(x) = 27 is to rewrite both sides as powers of _______.

Correct Answer: 3

Question 8:

If you cannot make the bases equal, you must use _______ to solve the exponential equation.

Correct Answer: logarithms

Question 9:

When distributing an exponent over parentheses, you are using the ________ property.

Correct Answer: distributive

Question 10:

When a base is raised to the zero power, it is equal to _______.

Correct Answer: 1

Educational Standards

A2.A.1.2:Use mathematical models to represent exponential relationships, such as compound interest, depreciation, and population growth. Solve these equations algebraically or graphically (including graphing calculator or other appropriate technology). A2.A.2.5:Rewrite algebraic expressions involving radicals and rational exponents using the properties of exponents.

Teaching Materials

Download ready-to-use materials for this lesson:

Student Worksheet Classroom Slides Assessment Quiz
Add to Google Classroom

User Actions

Sign in to save this lesson plan to your favorites.

Sign In

Share This Lesson

Related Lesson Plans