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6.2A – Solving Exponential Equations and Inequalities Objective: TSW solve exponential equations and inequalities. 1 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. 2 To Solve Exponential Equations: 1. Rewrite the Equation/Inequality so that the BASES are the same number. a. b. 2. 3. 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! 3 Examples…Solve and verify your answer 1. 32x = 81 2. 2x = 83 4 3. 92x-1 = 36x 4. 42n-1 = 64 5 5. (½)x = 42 – x 6. 3y + 2 = 1/27 6 Let’s Try a Couple Inequalities Now 7. 32x-1 > 1/243 8. 2x+2 > 1/32 7 Homework Time… pgs. 488-489 #’s 1-4(all), 814(evens), 25-29(odds), 32-34(all) 8