Math Skills Overview Guide
- Negative Numbers
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- Adding and Subtracting Whole Numbers
- Multiplying and Dividing Positive and Negative Whole Numbers
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- Order of Operations
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- Understanding Fractions
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- Using Conversion Ratios
- Introduction to Exponents
- Rules of Exponents
- Square Roots
- Definition of Exponents & Radicals
- Graphing Exponents
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- Writing Equations
Word Problems- Exponential
video, practice problems.
- Scientific Notation
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- Introduction to Linear Equations
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- Graphing Inequalities
- Systems of Linear Equations
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- Quadratic Equation
- Graphing the Quadratic Equation
- Solve the Quadratic Equation by Extracting Roots
- Solve the Quadratic Equation by Factoring
- Solve the Quadratic Equation by the Quadratic Formula
- Introduction to Functions
- Linear Functions
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- Variations: Direct & Inverse
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- Introduction to Logarithms
- Exponential & Logarithmic Functions
- Imaginary Numbers
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- Introduction to Matrices
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- Introduction to Trigonometry
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Exponential Growth and Decay Word Problems
Watch a Khan Academy Video » Length: 7:22
- Interpret change in exponential models
- Exponential vs. linear models
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Home > Math Worksheets > Algebra Worksheets > Solving Exponential Equations
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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Print solving exponential equations worksheets, click the buttons to print each worksheet and associated answer key., 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:  (x+1) = 625
Practice Worksheet 1
Solve these 10 exponential equations. Example:  (x+2) = 225
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:  (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:  (x+3) = 441. A scoring key is provided at the bottom to help you track your scores.
Do Now Pack
Complete the problems. Put your answer in the "My Answer" box. Example: 5 (5x-11) = 625
Lacking a Common Base Lesson
Learn how to solve the following problem: Solve the exponential equation 5 d = 22
Lacking a Common Base Worksheet
You will solve problems that do not have a set common base.
These problems go off in a more advanced type of an equation for students to work with.
Follow the steps to solve the following problem: Solve the exponential equation 11 d = 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 Quiz
We see how students did with this skill in a informal quiz.
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.
log 4 y -1=log 16
(y-1)log 4 = log 16
Applying the division rule to both sides, you can simplify log values on both sides.
(y - 1)log 4 /log 4 =log 16 / log 4
y - 1 = log 4
Simplify it further to evaluate the value of the variable.
y - 1 + 1 = log 4 + 1
y = log 4 + 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.
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Unit 2: Solving equations & inequalities
About this unit, linear equations with variables on both sides.
- Why we do the same thing to both sides: Variable on both sides (Opens a modal)
- Intro to equations with variables on both sides (Opens a modal)
- Equations with variables on both sides: 20-7x=6x-6 (Opens a modal)
- Equation with variables on both sides: fractions (Opens a modal)
- Equation with the variable in the denominator (Opens a modal)
- Equations with variables on both sides Get 3 of 4 questions to level up!
- Equations with variables on both sides: decimals & fractions Get 3 of 4 questions to level up!
Linear equations with parentheses
- Equations with parentheses (Opens a modal)
- Reasoning with linear equations (Opens a modal)
- Multi-step equations review (Opens a modal)
- Equations with parentheses Get 3 of 4 questions to level up!
- Equations with parentheses: decimals & fractions Get 3 of 4 questions to level up!
- Reasoning with linear equations Get 3 of 4 questions to level up!
Analyzing the number of solutions to linear equations
- Number of solutions to equations (Opens a modal)
- Worked example: number of solutions to equations (Opens a modal)
- Creating an equation with no solutions (Opens a modal)
- Creating an equation with infinitely many solutions (Opens a modal)
- Number of solutions to equations Get 3 of 4 questions to level up!
- Number of solutions to equations challenge Get 3 of 4 questions to level up!
Linear equations with unknown coefficients
- Linear equations with unknown coefficients (Opens a modal)
- Why is algebra important to learn? (Opens a modal)
- Linear equations with unknown coefficients Get 3 of 4 questions to level up!
- Inequalities with variables on both sides (Opens a modal)
- Inequalities with variables on both sides (with parentheses) (Opens a modal)
- Multi-step inequalities (Opens a modal)
- Using inequalities to solve problems (Opens a modal)
- Multi-step linear inequalities Get 3 of 4 questions to level up!
- Using inequalities to solve problems Get 3 of 4 questions to level up!
- Compound inequalities: OR (Opens a modal)
- Compound inequalities: AND (Opens a modal)
- A compound inequality with no solution (Opens a modal)
- Double inequalities (Opens a modal)
- Compound inequalities examples (Opens a modal)
- Compound inequalities review (Opens a modal)
- Solving equations & inequalities: FAQ (Opens a modal)
- Compound inequalities Get 3 of 4 questions to level up!
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Exponential Equations And Inequalities
Exponential Equations And Inequalities - Displaying top 8 worksheets found for this concept.
Some of the worksheets for this concept are Exponential equations not requiring logarithms, Solving exponential equations, Exponential equations and inequalities, Logarithmic equations and inequalities, Solve exponential equations and inequalities answer key, Solving exponential and logarithmic equations, Infinite algebra 2, Exponential log equations.
Found worksheet you are looking for? To download/print, click on pop-out icon or print icon to worksheet to print or download. Worksheet will open in a new window. You can & download or print using the browser document reader options.
1. Exponential Equations Not Requiring Logarithms
2. solving exponential equations, 3. 6.3 exponential equations and inequalities, 4. 6.4 logarithmic equations and inequalities, 5. solve exponential equations and inequalities answer key, 6. solving exponential and logarithmic equations, 7. infinite algebra 2, 8. exponential & log equations.
Solving Inequality Word Questions
(You might like to read Introduction to Inequalities and Solving Inequalities first.)
In Algebra we have "inequality" questions like:
Sam and Alex play in the same soccer team. Last Saturday Alex scored 3 more goals than Sam, but together they scored less than 9 goals. What are the possible number of goals Alex scored?
How do we solve them?
The trick is to break the solution into two parts:
Turn the English into Algebra.
Then use Algebra to solve.
Turning English into Algebra
To turn the English into Algebra it helps to:
- Read the whole thing first
- Do a sketch if needed
- Assign letters for the values
- Find or work out formulas
We should also write down what is actually being asked for , so we know where we are going and when we have arrived!
The best way to learn this is by example, so let's try our first example:
- the number of goals Alex scored: A
- the number of goals Sam scored: S
We know that Alex scored 3 more goals than Sam did, so: A = S + 3
And we know that together they scored less than 9 goals: S + A < 9
We are being asked for how many goals Alex might have scored: A
Sam scored less than 3 goals, which means that Sam could have scored 0, 1 or 2 goals.
Alex scored 3 more goals than Sam did, so Alex could have scored 3, 4, or 5 goals .
- When S = 0, then A = 3 and S + A = 3, and 3 < 9 is correct
- When S = 1, then A = 4 and S + A = 5, and 5 < 9 is correct
- When S = 2, then A = 5 and S + A = 7, and 7 < 9 is correct
- (But when S = 3, then A = 6 and S + A = 9, and 9 < 9 is incorrect)
Lots More Examples!
Example: Of 8 pups, there are more girls than boys. How many girl pups could there be?
- the number of girls: g
- the number of boys: b
We know that there are 8 pups, so: g + b = 8, which can be rearranged to
We also know there are more girls than boys, so:
We are being asked for the number of girl pups: g
So there could be 5, 6, 7 or 8 girl pups.
Could there be 8 girl pups? Then there would be no boys at all, and the question isn't clear on that point (sometimes questions are like that).
- When g = 8, then b = 0 and g > b is correct (but is b = 0 allowed?)
- When g = 7, then b = 1 and g > b is correct
- When g = 6, then b = 2 and g > b is correct
- When g = 5, then b = 3 and g > b is correct
- (But if g = 4, then b = 4 and g > b is incorrect)
A speedy example:
Example: Joe enters a race where he has to cycle and run. He cycles a distance of 25 km, and then runs for 20 km. His average running speed is half of his average cycling speed. Joe completes the race in less than 2½ hours, what can we say about his average speeds?
- Average running speed: s
- So average cycling speed: 2s
- Speed = Distance Time
- Which can be rearranged to: Time = Distance Speed
We are being asked for his average speeds: s and 2s
The race is divided into two parts:
- Distance = 25 km
- Average speed = 2s km/h
- So Time = Distance Average Speed = 25 2s hours
- Distance = 20 km
- Average speed = s km/h
- So Time = Distance Average Speed = 20 s hours
Joe completes the race in less than 2½ hours
- The total time < 2½
- 25 2s + 20 s < 2½
So his average speed running is greater than 13 km/h and his average speed cycling is greater than 26 km/h
In this example we get to use two inequalities at once:
Example: The velocity v m/s of a ball thrown directly up in the air is given by v = 20 − 10t , where t is the time in seconds. At what times will the velocity be between 10 m/s and 15 m/s?
- velocity in m/s: v
- the time in seconds: t
- v = 20 − 10t
We are being asked for the time t when v is between 5 and 15 m/s:
So the velocity is between 10 m/s and 15 m/s between 0.5 and 1 second after.
And a reasonably hard example to finish with:
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Most Used Actions
- How do you solve exponential inequalities?
- To solve exponential inequalities, write the inequality in the form of a single exponential function with a positive base. Take the logarithm of both sides of the inequality. Simplify the logarithmic expression to isolate the variable. Solve the inequality for the variable. Check the solution by plugging it back into the original inequality.
- What is exponential inequality?
- An exponential inequality is an inequality that involves one or more exponents.
- How do you solve exponential inequalities with fractions?
- To solve exponential inequalities with fractions, first convert the fractions to powers of the base using the properties of exponents. Then, apply the usual methods for solving exponential inequalities.
- High School Math Solutions – Inequalities Calculator, Exponential Inequalities Last post, we talked about how to solve logarithmic inequalities. This post, we will learn how to solve exponential... Read More