These worksheets demonstrate the steps required to solve exponential equations and give practice problems to help students master the skill. We cover the common types of problems you run into with these worksheets. There are two main types of difference between exponential equations problems, and it entirely depends on the bases. If the bases are the same, the problem is most likely pretty easy. If the bases differ that can really complicate things. The first step is usually to set the exponents equal to one another when the bases are the same. Next step is to solve for the unknown variable. Once you do that your answer is within your grasp.
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Solving Exponential Equations Lesson
This starts with a full lesson how to manipulate these types of equations. Learn how to solve problems like the following: Solve the exponential equation: [25](x+1) = 625
Worksheet 2
you will work on solving 10 exponential equations. These problems are a bit more challenging. Example: 4(x+3) = 256
Solving Exponential Equations Review Sheet
Follow the steps to solve the following problem: [221](x-5) = 49. Afterwards, practice the skill by completing six similar problems.
Full Topic Quiz
Solve these 10 exponential equations and then score your answers. Example: [21](x+3) = 441. A scoring key is provided at the bottom to help you track your scores.
Lacking a Common Base Lesson
Learn how to solve the following problem: Solve the exponential equation 5d = 22
Review Section
Follow the steps to solve the following problem: Solve the exponential equation 11d = 23. Then practice the skill by solving the problems given. This serves as a review of all the skills that we have learned.
No Common Base Do Now
this is a good way to either introduce or review this skill with your class. They will be able to plot how they completed the problem and how it should be done, if they fell off the path.
How to Solve Exponential Equations
Teaching algebra to kids can be exhausting. The introduction of variables makes it difficult for them to understand equations. One of the primary challenges is to teach the students how to solve exponential equations. If your class's kids struggle with solving exponential algebraic problems, we have a few methods to help you.
Before we jump into the ways of solving exponential equations, it is vital to understand what they are. Let's look at the formal definition of exponential equations.
What Are They?
Exponential equations refer to algebraic equations with a variable in the exponent position. To solve such problems, you need to evaluate the value of exponents. For example, the equation 4 = 2x is an exponential equation.
Equating Same Bases
When you have to solve an exponential equation, see if the two sides of the equation have the same base value. In such cases, you can directly ignore the bases and evaluate exponential values.
For example, if you have to solve 43y = 46, you can ignore the same base on both sides and simplify the equation as 3y = 6.
We ignore the same base values due to their equality. If we apply logic to it, two bases with the same values on both sides of the equation are equal. We only need to work on the exponential part of the equation. By simplifying the exponents on both sides, we can evaluate the answer. You can test the accuracy of your solution by inputting the answer into the exponential variable.
Equating Exponent With Whole Number
In some cases, you may come across equations with an exponential expression on one side and a whole number on the other side of the equation. To simplify such algebraic equations, you can eliminate the exponent's base value and equate it with the whole number on the other side.
For example, if you find an equation 2y + 1 + 4 = 8, you can apply the subtraction rule on both sides to equate the exponential value against the whole number. Here is how you can simplify it:
2y + 1 + 4 - 4 = 8 - 4
2y + 1 = 4
Using this method, you can change the whole number into a similar expression as on the other side of the equation to get the value for the variable.
2y + 1 = 22
Now you can ignore the same base values on both sides and simplify the equation to find the variable's value.
Use Log for Different Bases
To apply this method, you must have all the exponential values isolated on one side of the equation and the whole number on the other. Once done, you can apply the addition or subtraction rule to both sides for simplification.
For example, if you have an equation, 4y - 2 - 8 = 8, you can apply the addition rule like this:
4y - 1 - 8 + 8 = 8 + 8
4y - 1 = 16
Since you do not have the same base values on both sides of the equation, you can apply a log on both sides.
log4y -1=log16
(y-1)log4 = log16
Applying the division rule to both sides, you can simplify log values on both sides.
(y - 1)log4/log4 =log16 / log4
y - 1 = log4
Simplify it further to evaluate the value of the variable.
y - 1 + 1 = log4 + 1
y = log4 + 1
y = 0.6020 + 1
y = 1.6020
Using the methods mentioned above, you can solve exponential equations quickly. If you want to teach your students all three ways, you can find several exponential equations online to test their learning. You may also come up with some of your exponential algebraic equations to improve the skills of your students.
Exponents always can complicate equations, not because it complicates the concepts, but it does make the calculations more difficult for students. This series of worksheets will work on how to solve for exponential variables in algebraic expressions through the use of logarithmic tables and by balancing the equation. The complete set contains all introductory material, practice questions, reviews, longer exercise sheets, and quizzes. We will walk through the vocabulary and set you in the right direction to process these types of problems. This series of problems will normally require you to calculate and take many different thoughts into consideration before approaching problems like this. Exponents are the backbone of the problems and need to be kept in the back of your mind when you choose each step of your process. These problems often have the variable located within the exponent with heightens the difficult and conceptualization of the problem itself.