Exponential EquationsDefinition, Solving, and Examples
In arithmetic, an exponential equation takes place when the variable shows up in the exponential function. This can be a scary topic for kids, but with a bit of instruction and practice, exponential equations can be worked out easily.
This article post will discuss the definition of exponential equations, types of exponential equations, proceduce to figure out exponential equations, and examples with solutions. Let's get right to it!
What Is an Exponential Equation?
The primary step to work on an exponential equation is knowing when you are working with one.
Definition
Exponential equations are equations that consist of the variable in an exponent. For instance, 2x+1=0 is not an exponential equation, but 2x+1=0 is an exponential equation.
There are two primary items to look 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, take a look at this equation:
y = 3x2 + 7
The primary thing you should notice is that the variable, x, is in an exponent. The second thing you must not is that there is one more term, 3x2, that has the variable in it – not only in an exponent. This signifies that this equation is NOT exponential.
On the contrary, take a look at this equation:
y = 2x + 5
Yet again, the primary thing you must note is that the variable, x, is an exponent. Thereafter thing you must note is that there are no other terms that includes any variable in them. This implies that this equation IS exponential.
You will come upon exponential equations when working on diverse calculations in algebra, compound interest, exponential growth or decay, and other functions.
Exponential equations are very important in math and play a pivotal role in working out many computational questions. Hence, it is critical to completely grasp what exponential equations are and how they can be used as you go ahead in arithmetic.
Kinds of Exponential Equations
Variables occur in the exponent of an exponential equation. Exponential equations are remarkable ordinary in everyday life. There are three major types of exponential equations that we can solve:
1) Equations with identical bases on both sides. This is the simplest to solve, as we can easily set the two equations equal to each other and solve for the unknown variable.
2) Equations with distinct bases on both sides, but they can be created similar employing properties of the exponents. We will take a look at some examples below, but by changing the bases the same, you can observe the described steps as the first event.
3) Equations with variable bases on both sides that is unable to be made the similar. These are the trickiest to figure out, but it’s possible using the property of the product rule. By increasing two or more factors to the same power, we can multiply the factors on both side and raise them.
Once we are done, we can set the two latest equations identical to each other and figure out the unknown variable. This article does not contain logarithm solutions, but we will tell you where to get guidance at the very last of this article.
How to Solve Exponential Equations
From the explanation and kinds of exponential equations, we can now learn to work on any equation by following these easy procedures.
Steps for Solving Exponential Equations
We have three steps that we need to follow to work on exponential equations.
Primarily, we must determine the base and exponent variables within the equation.
Next, we need to rewrite an exponential equation, so all terms are in common base. Subsequently, we can solve them using 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 original equation to find the value of the other.
Examples of How to Solve Exponential Equations
Let's look at some examples to note how these steps work in practicality.
First, we will work on the following example:
7y + 1 = 73y
We can see that all the bases are the same. Thus, all you have to do is to restate the exponents and solve 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 real:
71/2 + 1 = 73(½)
73/2=73/2
Let's observe this up with a further complicated question. Let's solve this expression:
256=4x−5
As you can see, the sides of the equation does not share a common base. But, both sides are powers of two. By itself, the working comprises of breaking down respectively 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 ultimate result:
28=22x-10
Apply algebra to figure out x in the exponents as we conducted in the previous example.
8=2x-10
x=9
We can verify our answer by replacing 9 for x in the original equation.
256=49−5=44
Continue seeking for examples and problems on the internet, and if you utilize the laws of exponents, you will turn into a master of these concepts, working out most exponential equations without issue.
Improve Your Algebra Abilities with Grade Potential
Solving questions with exponential equations can be difficult with lack of guidance. Even though this guide goes through the basics, you still may encounter questions or word problems that may hinder you. Or maybe you require some additional help as logarithms come into the scenario.
If this sounds like you, contemplate signing up for a tutoring session with Grade Potential. One of our expert teachers can guide you improve your abilities and confidence, so you can give your next exam a grade-A effort!
