Before you try to solve exponential equations, you must be quite comfortable using the rules and laws of exponents. An exponential equation is simply an equation in which a variable appears in the exponent.
Examples of exponential equations
2x = 4
22x = 16
2x + 1 = 256
Steps to solve exponential equations
There are many different kinds of exponential equations. First, let's focus on exponential equations that have a single term on both sides. These equations can be classified into two different types.
Type #1) When the bases are of both terms are the same
Type #2) When the bases are of the terms are different
Solving Exponential Equations of the same base (type #1)
Let's solve the following exponential equation: 4x+1 = 49
Step 1)Ignore the bases, and simply set the exponents equal to each other
1) X+ 1 = 9
Step 2) Solve for the variable
2) X = 9 − 1
X = 8
Solving Exponential Equations of with unlike bases (type #2)
Let's solve : 43 =2x
1) Ignore the exponents and Answer the following question: "4 and 2 are powers of what number? " Once you have your answer, rewrite both of the bases as powers of that number
1) They are both powers of 2
4 = 2²
2) Substitute the rewritten larger base into the equation
Demonstration Problem 2: Solving Exponential Equations
Exponential Equations with Negative Exponents
It is possible to use the steps outlined on this page to solve exponential equations with negative exponents. Again, it is necessary that both of the bases are powers of a common base.