6.2A – Solving Exponential Equations and Inequalities

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Presentation transcript:

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

Exponential Equation – unknown variables are the exponents. 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.

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!

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

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

5. (½)x = 42 – x 6. 3y + 2 = 1/27

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

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