Exponential Equations

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1Simplifying Expressions Review

Steps to Writing & Solving Exponential Equations or Inequalities

Examples

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Simplifying Exponential Expressions

All rules for exponents apply

2 7(4 )x

144 x

2 9(7 )

187

3 27

5 32 2

5 32

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Solving Exponential Equations/Inequalities

Steps Make the base numbers equal on both

sides using the rules of exponents Set the exponents equal to each other Solve for the variable Check Your Answers!

Not all equations/inequalities are solvable

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Example for Solving Exponential Equations

Solve 2 13 81n

2 13 81n 2 1 43 3n

2 1 4n 2 3n

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2n

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Another Example for Solving Exponential Equations

Solve 14 8x x

14 8x x2 3 1(2 ) (2 )x x

2 3 3x x 3x

3x 2 3 32 2x x

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Example for Solving Exponential Inequalities

Solve 3 1 14

256p

3 1 14

256p

3 1 44 4p

3 1 4p

3 3p

1p

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What if the bases wont’ match?

Now you get to use the “log” function of your calculator

Steps: Take the log (base 10) of each side Use the powers rule Isolate the variable algebraically Usually division Solve for the variable

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Example

Solve 285153 x

285153 x

285log15log 3 x

285log15log3 x

15log

285log

15log

15log3

x15log

285log3 x

15log3

285log

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3x

15log3

285logx

6958.x