Solve Exponential Equations

Examples of exponential equations

• 2^x = 4
• 2^2x = 16
• 2^{x + 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: 4^x+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 =2^x

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	2) 43 =2x (22)3 =2x
3) Simplify	3) 26 = 2x
4) Solve like an exponential equation of like bases	4) 6 = x

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.

---