Exponential EquationsExplanation, Workings, and Examples
In arithmetic, an exponential equation occurs when the variable appears in the exponential function. This can be a terrifying topic for children, but with a some of instruction and practice, exponential equations can be worked out simply.
This article post will talk about the definition of exponential equations, types of exponential equations, steps to work out exponential equations, and examples with answers. Let's began!
What Is an Exponential Equation?
The first step to solving an exponential equation is determining when you have one.
Definition
Exponential equations are equations that consist of 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 keep in mind for when trying to determine if an equation is exponential:
1. The variable is in an exponent (meaning it is raised to a power)
2. There is only one term that has the variable in it (besides the exponent)
For example, take a look at this equation:
y = 3x2 + 7
The most important thing you must note is that the variable, x, is in an exponent. The second thing you must notice is that there is another term, 3x2, that has the variable in it – just not in an exponent. This implies that this equation is NOT exponential.
On the contrary, take a look at this equation:
y = 2x + 5
Yet again, the first thing you should note is that the variable, x, is an exponent. Thereafter thing you should notice is that there are no other value that consists of any variable in them. This means that this equation IS exponential.
You will come upon exponential equations when you try solving different calculations in exponential growth, algebra, compound interest or decay, and other functions.
Exponential equations are crucial in math and play a central responsibility in working out many computational questions. Thus, it is critical to completely understand what exponential equations are and how they can be utilized as you go ahead in arithmetic.
Kinds of Exponential Equations
Variables come in the exponent of an exponential equation. Exponential equations are remarkable easy to find in everyday life. There are three major types of exponential equations that we can solve:
1) Equations with the same bases on both sides. This is the simplest to work out, as we can simply set the two equations equivalent as each other and figure out for the unknown variable.
2) Equations with dissimilar bases on each sides, but they can be created similar utilizing rules of the exponents. We will put a few examples below, but by converting the bases the equal, you can follow the exact steps as the first case.
3) Equations with distinct bases on both sides that cannot be made the similar. These are the most difficult to work out, but it’s feasible through the property of the product rule. By increasing both factors to identical power, we can multiply the factors on both side and raise them.
Once we have done this, we can determine the two latest equations identical to each other and figure out the unknown variable. This article do not cover logarithm solutions, but we will let you know where to get assistance at the end of this blog.
How to Solve Exponential Equations
After going through the definition and types of exponential equations, we can now learn to work on any equation by following these simple steps.
Steps for Solving Exponential Equations
We have three steps that we are required to ensue to solve exponential equations.
First, we must identify the base and exponent variables in the equation.
Second, we need to rewrite an exponential equation, so all terms are in common base. Thereafter, we can work on them utilizing standard algebraic methods.
Third, we have to solve for the unknown variable. Now that we have figured out the variable, we can put this value back into our original equation to discover the value of the other.
Examples of How to Solve Exponential Equations
Let's take a loot at some examples to see how these procedures work in practicality.
Let’s start, we will work on the following example:
7y + 1 = 73y
We can observe that both bases are identical. Thus, all you need to do is to rewrite the exponents and work on them through algebra:
y+1=3y
y=½
Right away, we substitute the value of y in the given equation to support that the form is real:
71/2 + 1 = 73(½)
73/2=73/2
Let's observe this up with a further complicated question. Let's figure out this expression:
256=4x−5
As you have noticed, the sides of the equation does not share a common base. But, both sides are powers of two. As such, the solution comprises of decomposing respectively the 4 and the 256, and we can alter the terms as follows:
28=22(x-5)
Now we work on this expression to find the final answer:
28=22x-10
Perform algebra to work out the x in the exponents as we did in the last example.
8=2x-10
x=9
We can recheck our answer by substituting 9 for x in the initial equation.
256=49−5=44
Keep searching for examples and questions on the internet, and if you utilize the laws of exponents, you will become a master of these concepts, solving most exponential equations with no issue at all.
Level Up Your Algebra Skills with Grade Potential
Working on questions with exponential equations can be tricky without guidance. While this guide covers the fundamentals, you still might encounter questions or word problems that might stumble you. Or perhaps you require some additional assistance as logarithms come into the scene.
If this sounds like you, contemplate signing up for a tutoring session with Grade Potential. One of our professional tutors can guide you enhance your abilities and confidence, so you can give your next test a grade-A effort!
