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Your warm up is on the back table. Please get started. We’ll go over it in a minute.

Welcome to class. Your warm up is on the back table. Please get started. We’ll go over it in a minute. Solving Exponential Equations. 4 2x + 3 = 1. Definition. An exponential equation is an equation in which a variable appears in the exponent. Examples of exponential equations

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Your warm up is on the back table. Please get started. We’ll go over it in a minute.

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  1. Welcome to class • Your warm up is on the back table. • Please get started. • We’ll go over it in a minute.

  2. Solving Exponential Equations 4 2x + 3 = 1

  3. Definition An exponential equationis an equation in which a variable appears in the exponent. Examples of exponential equations 2x = 4 22x = 16 2x + 1 = 256

  4. Types of exponential equations There are many different kinds of exponential equations. Today, we’ll 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

  5. Type #1) When the bases of both terms are the same, solve by equating exponents Bases are the same Equate the exponents Solve Check Sweet

  6. Let me show you again Bases are the same 53 – 2x = 5-x 3 – 2x = -x Equate the exponents 3 = x Solve • 53 – 2(3) = 5-3 • 53 – 6= 5-3 • 5-3 = 5-3 Nice Check

  7. Bases are the same Your turn Equate the exponents Check Solve Whiteboards

  8. 0 0 9 0 0 0 2 3 8 6 5 4 3 2 1 7 0 9 5 1 8 7 6 5 4 3 2 3 0 4 9 8 7 6 5 4 1 2 3 9 8 7 6 5 4 2 7 1 0 2 1 9 8 6 1 5 0 0 3 2 1 0 4 8 9 6 5 4 3 2 1 0 7 McAnelly’s Incredibly Awesome Timer Hours Minutes Seconds

  9. 0 0 9 0 0 0 1 3 8 6 5 4 3 2 1 7 0 9 5 1 8 7 6 5 4 3 2 3 0 4 9 8 7 6 5 4 0 2 3 9 8 7 6 5 4 2 7 1 0 2 1 9 8 6 1 5 0 0 3 2 1 0 4 8 9 6 5 4 3 2 1 0 7 McAnelly’s Incredibly Awesome Timer Hours Minutes Seconds

  10. Bases are the same Your turn Equate the exponents Check Solve X = -2 X = 6 X = -8

  11. Type #2) When the bases are different , rewrite the expressions to have the same base Rewrite so that bases are the same 2(3x) = 3(x + 1) Equate the exponents 6x = 3x + 3 Solve Check Beautiful

  12. Let me show you again Rewrite so that bases are the same 22(3) = 2x 43 =2x Equate the exponents 2(3) = x 6 = x Solve • 43 = 26 • 22(3)= 26 • 26 = 26 Check Easy

  13. Let’s kick it up a notch Rewrite so that bases are the same 32-r = 30 32-r = 1 Equate the exponents 2-r = 0 r = 2 Solve 32-2 = 1 • 30 = 1 • 1 = 1 Check Woot

  14. REWRITE so bases are the same Your turn Grab a calculator Equate the exponents Solve Check X = 11 3 X = -6 X = 30

  15. One for the money • Solve this on your board. • Turn it over when you are done. • I will walk around and check. 36(x+2) = 216(x-1) Rewrite so that bases are the same 62(x+2) = 63(x-1) 36(7+2) = 216(7-1) Equate the exponents 369= 2166 2(x+2) = 3(x-1) Verified with calculator Solve 2x+4 = 3x-3 Check x= 7

  16. Your assignment Solving Exponential Equations - EASY

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