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6.2A – Solving Exponential Equations and Inequalities

6.2A – Solving Exponential Equations and Inequalities. Objective: TSW solve exponential equations and inequalities. Some Notes…. Exponential Equation – unknown variables are the exponents. If two powers are equal and they have the same base, then the exponents must be the same

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6.2A – Solving Exponential Equations and Inequalities

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  1. 6.2A – Solving Exponential Equations and Inequalities Objective: TSW solve exponential equations and inequalities.

  2. Some Notes… • Exponential Equation – unknown variables are the exponents. • If two powers are equal and they have the same base, then the exponents must be the same • ex. if bx = ay and a = b, then x = y. • If two powers are equal and they have the same exponents, then the bases must be the same • ex. if bx = ay and x = y, then a = b.

  3. To Solve Exponential Equations: • Rewrite the Equation/Inequality so that the BASES are the same number. • If the base is a number, just break it down with a factor tree. • If the base is a fraction, FIRST write as a whole number by using negative exponents. • Once the bases are equal, you can set the exponents equal to each other and solve. • Check your solution!

  4. Examples…Solve and verify your answer 1. 32x = 81 2. 2x = 83

  5. 3. 92x-1 = 36x 4. 42n-1 = 64

  6. 5. (½)x = 42 – x 6. 3y + 2 = 1/27

  7. Let’s Try a Couple Inequalities Now  7. 32x-1 > 1/243 8. 2x+2 > 1/32

  8. Homework Time… pgs. 488-489 #’s 1-4(all), 8-14(evens), 25-29(odds), 32-34(all)

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