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chapter 1 45 - SECTION 1.6 lNVERSE FUNCTIONS AND L 46...

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Unformatted text preview: SECTION 1.6 lNVERSE FUNCTIONS AND LOGARITHMS 45 40 46. l><10'0 0 7><1015 From the graphs. we see that f(:n) = 360.1 > g(w) = lnx for approximately 0 < a: < 3.06. and then g(a:) > f(.’£) for 3.06 < m < 3.43 X 1015 (approximately). At that point. the graph off finally surpasses the graph ofg for good. 47. (a) Shift the graph of y : log10 a: five units to the (b) Reflect the graph of y : lna: about the m-axis left to obtain the graph of y = log10(a: + 5). to obtain the graph ofy : ~ lnx. Note the vertical asymptote of ac : —5. y = In a; y : — lnm y : logic 33 y :10g10($ ‘l' 5) y y y 0 l E 0 l 3 0 l 7 48. (a) Reflect the graph of y = ln 2: about the y-axis to (b) Reflect the portion of the graph of y : 1n 9: to obtain the graph of y : In (—50) the right of the y—axis about the y—axis. The 3/ : 111$ y : 1n(—;y) graph of y = ln |ac| is that reflection in addition y to the original portion. y 2 In a: y = ln [ml 0 1 J: y 0 1 —; 49-(a)21H$—1 ‘5 lnx~§ —> 33*61/2—«5 (b)e‘m*5 A m 1115 m ln5 50.(a)e2$+377:0 => 62w+327 => 2$+3—ln7 2x—ln7 3 _> m_§(1n7—3) (b)ln(5—2$)——3 —> 5 2$~e_3 2xa5—e_3 => m=§(5ie*3) 51. (2021423 <=> log232m~5 c» m:5+log23. 0r:21*5=3 4: 1n(2$*5)—1n3 (x 5)in2_1n3 s—> x—5:ln—3 c» m=5+ln—3 ln2 1112 (b) 111m + ln(;c i 1) : ln(a:(a: — 1)) = 1 (a) 20(3: ~ 1): e1 (a) :02 — w ~ 6 : O. The quadratic formula (with a : 1. b 2 —1, and c = —e) gives a: = %(1 :l: x/l + 46), but we reject the negative root since the natural logarithm is not defined for ac < 0. So 5c : %(1 + (/1 + 4e). ...
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