Solve Exponential Equations

Examples of expontial 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 Expontial 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 = 15
Step 2) Solve for the variable	2) X = 15 − 1   X = 14

Solving Expontial 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

Answer

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