Solving Exponential Equations With the Same Base: Free Color by Number

algebra 2

Want the free Exponential Equations color by number? Click here

Solving exponential equations with the same base is one of the first places Algebra 2 students use the properties of exponents for real, and here is the activity I use to practice it, free: a color by number with 12 exponential equations, an answer bank, a coloring page and an answer key.

Below is how I teach the method and how I run the activity. Type your email on the sign-up page and the PDF is yours right away.

How to solve exponential equations with the same base

If two powers of the same base are equal, their exponents are equal. So the whole method is to write both sides as powers of the same base, set the exponents equal, and solve the equation that is left.

Here is one: 8^(x + 1) = 4^(2x). Both 8 and 4 are powers of 2, so write 8 as 23 and 4 as 22. That gives 2^(3x + 3) = 2^(4x). Set the exponents equal: 3x + 3 = 4x, so x = 3. Fractions work the same way, because 1/3 is 3^(-1): (1/3)^x = 27 becomes 3^(-x) = 33, so x = -3.

The first practice page of the Solving Exponential Equations coloring activity

The lesson at a glance

Grade: Algebra 2
Standard: Common Core HSA-SSE.B.3c: use the properties of exponents to transform expressions for exponential functions
You need: the two practice pages, the answer bank and the coloring page, one set per student, colored pencils, the answer key
Students will be able to: solve exponential equations by rewriting both sides with a common base

Get the free color by number and answer key

Before you teach

Print the two practice pages for each student, and keep the answer bank and the coloring page on your desk for now. Students will need colored pencils for the end.

The solving exponential equations activity: 12 equations

Students solve the 12 equations on the two practice pages. None of the bases match at the start, so students rewrite each side as a power of 2, 3, 5 or 6 first. Some problems have a fraction, like 1/4, so students use negative exponents too.

The answer bank: check before coloring

This is the part I would not skip. When students finish the problems, I hand them the answer bank to check that each answer is on it. That stops the guessing, and students fix their mistakes before they start coloring.

The coloring page

Each answer on the bank has a color. Students find the problem numbers on the picture and color each space to match. A wrong answer shows up as a color that does not belong.

The coloring page of the Solving Exponential Equations coloring activity

The answer key and the finished picture

The answer key shows every answer with its color, and the finished picture shows what the coloring page should look like.

Here is the free Exponential Equations color by number

Type your name and email on the sign-up page. The PDF downloads on the next page, and a copy comes to your inbox.

Get the free activity

More Algebra II in my membership: a prep unit and 8 units

Equations and Inequalities
Linear Relations and Functions
Systems of Equations and Inequalities
Quadratic Functions and Relations
Polynomials and Polynomial Functions
Inverses and Radical Functions and Relations
Exponential and Logarithmic Functions and Relations
Rational Functions and Relations

See every Algebra II lesson

Questions teachers ask about exponential equations

How do you solve exponential equations with the same base?

Set the exponents equal and solve. If 5^(2x) = 5^(x + 4), then 2x = x + 4, so x = 4.

How do you solve exponential equations with different bases?

Rewrite both sides as powers of a common base when you can, like 9 = 32 and 27 = 33, and then set the exponents equal. Every equation in this activity works that way. When there is no common base, students use logarithms, which come later.