Simplifying and Solving Exponential Equations is a fundamental skill in both Precalculus and Calculus.
Jenn, Founder Calcworkshop®, 15+ Years Experience (Licensed & Certified Teacher)
An Exponential Function is when the variable is the power and not the base.
This means we will need tricks in order to determine what the variable equals, that go beyond our normal rules for solving equations.
Rule of Exponents for a Power of a Power
There are seven basic Exponential Properties:
- Power of Products
- Power of a Power
- Division of Powers
- Negative Powers
- Zero Power
- Rational Powers
- Equivalence of Powers
And by mastering these properties and knowing how to use them in Simplifying and Solving Exponential Equations, is like unlocking a huge treasure box.
We will take our exponential properties and apply them to our three-step process for solving Exponential Equations.
As Purple Math states, to solve exponential equations you need to have equations with comparable exponential expressions on either side of the “equals” sign, so you can compare the powers and solve.
What does this really mean?
Negative Exponent Rule
Well, we need to transform our equation in such a way as to have one term on the left-hand side of the equation and one term on the right-hand side of the equation, and where both of these terms have the same base.
When this happens, we have the power of equivalence, which means if the bases are the same then the exponents must be equal too.
Here’s the secret…
…The key to learning how to solving exponential equations efficiently can be is found in one really critical step!
And together we will walk through ten examples of how to use our exponential properties to simplify expressions and seven problems of where we will solve an Exponential Equation.
How to Solve Exponential Equations – Video
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