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Published byMuriel Osborne Modified over 9 years ago
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6.2A – Solving Exponential Equations and Inequalities
Objective: TSW solve exponential equations and inequalities.
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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.
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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!
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Examples…Solve and verify your answer
1. 32x = x = 83
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3. 92x-1 = 36x n-1 = 64
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5. (½)x = 42 – x y + 2 = 1/27
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Let’s Try a Couple Inequalities Now
7. 32x-1 > 1/ x+2 > 1/32
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Homework Time… pgs #’s 1-4(all), 8-14(evens), 25-29(odds), 32-34(all)
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