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Stitz-Zeager_College_Algebra_e-book

Then look up the rule of 72 and compare your answers

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Unformatted text preview: − log[H+ ] ≤ 8.5 or −7.8 ≥ log[H+ ] ≥ −8.5. To solve this compound inequality we solve −7.8 ≥ log[H+ ] and log[H+ ] ≥ −8.5 and take the intersection of the solution sets.3 The former inequality yields 0 < [H+ ] ≤ 10−7.8 and the latter yields [H+ ] ≥ 10−8.5 . Taking the intersection gives us our ﬁnal answer 10−8.5 ≤ [H+ ] ≤ 10−7.8 . (Your Chemistry professor may want the answer written as 3.16 × 10−9 ≤ [H+ ] ≤ 1.58 × 10−8 .) After carefully adjusting the viewing window on the graphing calculator we see that the graph of f (x) = − log(x) lies between the lines y = 7.8 and y = 8.5 on the interval [3.16 × 10−9 , 1.58 × 10−8 ]. The graphs of y = f (x) = − log(x), y = 7.8 and y = 8.5 We close this section by ﬁnding an inverse of a one-to-one function which involves logarithms. log(x) is one-to-one. Find a formula for f −1 (x) and 1 − log(x) check your answer graphically using your calculator. Solution. We ﬁrst write y = f (x) then interchange the x and y and solve for y . Example 6.4.4. The function f (x) = y = f (x) l...
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