Stitz-Zeager_College_Algebra_e-book

C what principal p should be invested so that the

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Unformatted text preview: 1 = 0. The latter gives log(x +1) = 1, or x + 1 = 101 , which admits x = 9. We select test values x so that x + 1 is a power of 10, √ and we obtain −1 < −0.9 < 0 < 10 − 1 < 9 < 99. Our sign diagram gives the solution to be (−1, 0] ∪ [9, ∞). The calculator indicates the graph of y = f (x) = x log(x + 1) is above y = g (x) = x on the solution intervals, and the graphs intersect at x = 0 and x = 9. (+) 0 (−) 0 (+) −1 0 9 y = f (x) = x log(x + 1) and y = g (x) = x Near x = 0 Near x = 9 Our next example revisits the concept of pH as ﬁrst introduced in the exercises in Section 6.1. 6.4 Logarithmic Equations and Inequalities 373 Example 6.4.3. In order to successfully breed Ippizuti ﬁsh the pH of a freshwater tank must be at least 7.8 but can be no more than 8.5. Determine the corresponding range of hydrogen ion concentration. Solution. Recall from Exercise 6c in Section 6.1 that pH = − log[H+ ] where [H+ ] is the hydrogen ion concentration in moles per liter. We require 7.8 ≤...
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