Stitz-Zeager_College_Algebra_e-book

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Unformatted text preview: ) x 2 3 3. (a) 7x−1 = e(x−1) ln(7) log(x + 2) (b) log3 (x + 2) = log(3) (d) log(x2 + 1) = 4. (a) log3 (12) ≈ 2.26186 (d) log4 (b) log5 (80) ≈ 2.72271 (c) log6 (72) ≈ 2.38685 − 1 ln(z ) 4 (c) 2 = ex ln( 3 ) ln(x2 + 1) ln(10) 1 ≈ −1.66096 10 (e) log 3 (1000) ≈ −13.52273 5 (f) log 2 (50) ≈ −9.64824 3 358 6.3 Exponential and Logarithmic Functions Exponential Equations and Inequalities In this section we will develop techniques for solving equations involving exponential functions. Suppose, for instance, we wanted to solve the equation 2x = 128. After a moment’s calculation, we find 128 = 27 , so we have 2x = 27 . The one-to-one property of exponential functions, detailed in Theorem 6.4, tells us that 2x = 27 if and only if x = 7. This means that not only is x = 7 a solution to 2x = 27 , it is the only solution. Now suppose we change the problem ever so slightly to 2x = 129. We could use one of the inverse properties of exponentials and logarithms listed in Theorem 6.3 to...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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