Exponential EquationsDefinition, Workings, and Examples
In mathematics, an exponential equation takes place when the variable shows up in the exponential function. This can be a scary topic for students, but with a bit of direction and practice, exponential equations can be worked out simply.
This article post will talk about the explanation 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 solving an exponential equation is knowing when you are working with 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 items to bear in mind for when attempting 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 no other term that has the variable in it (aside from 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 should notice 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 flipside, check out this equation:
y = 2x + 5
Once again, the primary thing you must notice is that the variable, x, is an exponent. The second thing you should observe is that there are no other terms that have the variable in them. This signifies that this equation IS exponential.
You will come across exponential equations when working on different calculations in algebra, compound interest, exponential growth or decay, and various distinct functions.
Exponential equations are very important in arithmetic and perform a central role in figuring out many math problems. Thus, it is critical to completely grasp what exponential equations are and how they can be used as you move ahead in mathematics.
Types of Exponential Equations
Variables appear in the exponent of an exponential equation. Exponential equations are remarkable easy to find in everyday life. There are three main kinds of exponential equations that we can figure out:
1) Equations with identical bases on both sides. This is the most convenient to solve, as we can simply set the two equations same as each other and work out for the unknown variable.
2) Equations with dissimilar bases on each sides, but they can be created the same employing properties of the exponents. We will put a few examples below, but by changing the bases the equal, you can observe the same steps as the first event.
3) Equations with distinct bases on each sides that cannot be made the similar. These are the trickiest to work out, but it’s feasible using the property of the product rule. By increasing both factors to the same power, we can multiply the factors on both side and raise them.
Once we have done this, we can resolute the two latest equations identical to each other and figure out the unknown variable. This article does not include logarithm solutions, but we will tell you where to get help at the end of this article.
How to Solve Exponential Equations
Knowing the definition and types of exponential equations, we can now move on to how to work on any equation by following these easy procedures.
Steps for Solving Exponential Equations
We have three steps that we are required to follow to work on exponential equations.
Primarily, we must identify the base and exponent variables in the equation.
Next, we are required to rewrite an exponential equation, so all terms have a common base. Thereafter, we can work on them utilizing standard algebraic rules.
Lastly, we have to figure out the unknown variable. Since we have figured out the variable, we can put this value back into our original equation to figure out the value of the other.
Examples of How to Work on Exponential Equations
Let's check out some examples to see how these steps work in practicality.
First, we will work on the following example:
7y + 1 = 73y
We can observe that all the bases are the same. Therefore, all you have to do is to rewrite the exponents and figure them out using algebra:
y+1=3y
y=½
Now, we substitute the value of y in the given equation to corroborate that the form is true:
71/2 + 1 = 73(½)
73/2=73/2
Let's observe this up with a more complex sum. Let's solve this expression:
256=4x−5
As you can see, the sides of the equation does not share a identical base. Despite that, both sides are powers of two. By itself, the solution includes breaking down both the 4 and the 256, and we can alter the terms as follows:
28=22(x-5)
Now we solve this expression to find the final result:
28=22x-10
Carry out algebra to work out the x in the exponents as we did in the last example.
8=2x-10
x=9
We can double-check our workings by altering 9 for x in the original equation.
256=49−5=44
Keep searching for examples and questions online, and if you use the properties of exponents, you will become a master of these theorems, working out almost all exponential equations with no issue at all.
Enhance Your Algebra Skills with Grade Potential
Solving questions with exponential equations can be tricky with lack of support. While this guide take you through the basics, you still may face questions or word questions that might stumble you. Or possibly you desire some further assistance as logarithms come into the scene.
If you feel the same, consider signing up for a tutoring session with Grade Potential. One of our experienced teachers can guide you improve your skills and mental state, so you can give your next examination a first class effort!
