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Solve Exponential Equations
How to solve exponential equations
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 expontial 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 Expontial 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 = 15
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| Step 2) Solve for the variable |
2) X = 15 − 1
X = 14
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Solving Expontial Equations of with unlike bases (type #2)
Let's solve : 43 =2x
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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
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| 3) Simplify |
3) 26 = 2x |
| 4) Solve like an exponential equation of like bases |
4) 6 = x |
Practice Problems: solving exponential equations
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