Exponential EquationsExplanation, Solving, and Examples
In arithmetic, an exponential equation occurs when the variable appears in the exponential function. This can be a frightening topic for children, but with a some of instruction and practice, exponential equations can be solved simply.
This article post will discuss the explanation of exponential equations, kinds of exponential equations, process to solve exponential equations, and examples with answers. Let's began!
What Is an Exponential Equation?
The initial step to work on an exponential equation is knowing when you have one.
Definition
Exponential equations are equations that have the variable in an exponent. For example, 2x+1=0 is not an exponential equation, but 2x+1=0 is an exponential equation.
There are two primary things to bear in mind for when trying to figure out if an equation is exponential:
1. The variable is in an exponent (signifying it is raised to a power)
2. There is only one term that has the variable in it (besides the exponent)
For example, check out this equation:
y = 3x2 + 7
The first thing you must note is that the variable, x, is in an exponent. Thereafter thing you must notice is that there is additional term, 3x2, that has the variable in it – just not in an exponent. This implies that this equation is NOT exponential.
On the other hand, check out this equation:
y = 2x + 5
Once again, the first thing you should notice is that the variable, x, is an exponent. The second thing you must observe is that there are no more terms that consists of any variable in them. This signifies that this equation IS exponential.
You will come across exponential equations when working on diverse calculations in exponential growth, algebra, compound interest or decay, and other functions.
Exponential equations are essential in arithmetic and perform a pivotal role in figuring out many mathematical problems. Thus, it is critical to fully grasp what exponential equations are and how they can be utilized as you move ahead in your math studies.
Varieties of Exponential Equations
Variables come in the exponent of an exponential equation. Exponential equations are remarkable ordinary in everyday life. There are three main types of exponential equations that we can solve:
1) Equations with the same bases on both sides. This is the most convenient to solve, as we can simply set the two equations equal to each other and work out for the unknown variable.
2) Equations with different bases on each sides, but they can be created similar employing rules of the exponents. We will put a few examples below, but by converting the bases the equal, you can observe the exact steps as the first event.
3) Equations with distinct bases on both sides that cannot be made the same. These are the most difficult to work out, but it’s attainable using the property of the product rule. By increasing two or more factors to identical power, we can multiply the factors on each side and raise them.
Once we are done, we can set the two new equations identical to one another and figure out the unknown variable. This article does not include logarithm solutions, but we will tell you where to get assistance at the closing parts of this article.
How to Solve Exponential Equations
From the explanation and types of exponential equations, we can now learn to solve any equation by following these simple procedures.
Steps for Solving Exponential Equations
There are three steps that we need to ensue to solve exponential equations.
Primarily, we must recognize the base and exponent variables in the equation.
Next, we need to rewrite an exponential equation, so all terms are in common base. Thereafter, we can solve them utilizing standard algebraic rules.
Third, we have to figure out the unknown variable. Since we have figured out the variable, we can plug this value back into our initial equation to figure out the value of the other.
Examples of How to Work on Exponential Equations
Let's look at some examples to see how these steps work in practice.
First, we will solve the following example:
7y + 1 = 73y
We can observe that all the bases are identical. Thus, all you need to do is to rewrite the exponents and figure them out through algebra:
y+1=3y
y=½
Right away, we replace the value of y in the respective equation to support that the form is true:
71/2 + 1 = 73(½)
73/2=73/2
Let's observe this up with a further complex problem. Let's solve this expression:
256=4x−5
As you have noticed, the sides of the equation does not share a identical base. However, both sides are powers of two. As such, the working includes decomposing both the 4 and the 256, and we can replace the terms as follows:
28=22(x-5)
Now we figure out this expression to find the final answer:
28=22x-10
Carry out algebra to figure out x in the exponents as we conducted in the previous example.
8=2x-10
x=9
We can double-check our workings by replacing 9 for x in the original equation.
256=49−5=44
Continue seeking for examples and problems online, and if you utilize the laws of exponents, you will inturn master of these theorems, figuring out almost all exponential equations without issue.
Better Your Algebra Abilities with Grade Potential
Working on questions with exponential equations can be difficult with lack of help. Although this guide take you through the fundamentals, you still might face questions or word questions that make you stumble. Or perhaps you need some extra guidance as logarithms come into the scenario.
If this sounds like you, think about signing up for a tutoring session with Grade Potential. One of our experienced tutors can guide you improve your abilities and confidence, so you can give your next exam a first class effort!
