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Section 3.4 Solving Exponential and Logarithmic Equations 227 11. Point of intersection: 4, 10 Algebraically: 5 x2 15 10 5 x2 25 5 2 −4 20 f g 8 x 2 2 −20 x 4 4, 10 12. f x 2 x1 3 13. gx 13 16 g f −12 12 0 Point of intersection: 3, 13 2 x1 3 13 2 x1 16 2 4 x 1 4 x 3 ⇒ 3, 13 30 g f −50 275 −5 Point of intersection: 243, 20 Algebraically: 4 log 3 x 20 log 3 x 5 x 3 5 243 243, 20 14. f x 3 log 5 x 3 ln x ln 5 gx 6 15. −9 g 6 f 9 −2 12 g f 28 −6 Point of intersection: 4, 3 Algebraically: ln e x1 2x 5 © Houghton Mifflin Company. All rights reserved. 16. −8 Point of intersection: 25, 6 3 log 5 x 6 log 5 x 2 x 5 2 25 ⇒ 25, 6 f x ln e x2 x 2 gx 3x 2 Point of intersection: 2, 4 x 2 3x 2 4 2x −9 f g 4 −8 9 4, 3 x 1 2x 5 4 x x 2 ⇒ 2, 4
228 Chapter 3 Exponential and Logarithmic Functions 17. 4 x 16 18. 3 19. 5 x 1 x 243 20. 625 4 x 4 2 3 x 3 5 5 x 2 x 1 x 5 5 4 54 x 4 7 x 1 49 7 x 7 2 x 2 21. 1 8 x 64 22. 23. 8 x 8 2 x 2 x 2 1 2 x 32 2 3 x 81 16 24. 1 2 x 1 2 5 3 2 x 3 2 4 x 5 x 4 x 4 3 4 x 27 64 3 4 x 3 4 3 x 3 25. 27. 610 x 216 26. 10 x 36 log 10 10 x log 10 36 x log 10 36 1.5563 2 x3 256 Alternate solution: 28. 2 x 2 3 256 2 x3 2 8 2 x 32 x 3 8 x 5 x 5 58 x 325 8 x 65 x log 8 65 3 x1 1 81 3 x1 3 4 x 1 4 ln 65 ln 8 2.0075 x 3 29. ln x ln 5 0 30. ln x ln 2 0 31. ln x 7 32. ln x 1 ln x ln 5 ln x ln 2 x e 7 e 1 x x 5 x 2 x 1 e 0.368 33. 36. log x 625 4 34. log x 25 2 35. x 4 625 x 4 5 4 x 5 log 10 x 1 2 x 10 12 1 10 0.316 37. x 2 25 x 5 ln2x 1 5 2x 1 e 5 x 1 e5 2 74.707 38. log 10 x 1 x 10 1 x 1 10 ln3x 5 8 e 8 3x 5 x 1 3 e8 5 991.986 © Houghton Mifflin Company. All rights reserved. 39. ln e x2 x 2 ln e x x 2 40. ln e 2x1 2x 1 41. e ln5x2 5x 2 42. e ln x2 x 2 43. 1 ln e 2x 1 2x 2x 1 44. 8 e ln x3 8 x 3 x 3 8
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Section 3.4 Solving Exponential and Logarithmic Equations 227<br />
11. Point of intersection: 4, 10<br />
Algebraically: 5 x2 15 10<br />
5 x2 25 5 2<br />
−4<br />
20<br />
f<br />
g<br />
8<br />
x 2 2<br />
−20<br />
x 4<br />
4, 10<br />
12.<br />
f x 2 x1 3 13.<br />
gx 13<br />
16<br />
g<br />
f<br />
−12<br />
12<br />
0<br />
Point of intersection: 3, 13<br />
2 x1 3 13<br />
2 x1 16 2 4<br />
x 1 4<br />
x 3 ⇒ 3, 13<br />
30<br />
g<br />
f<br />
−50<br />
275<br />
−5<br />
Point of intersection: 243, 20<br />
Algebraically: 4 log 3 x 20<br />
log 3 x 5<br />
x 3 5 243<br />
243, 20<br />
14.<br />
f x 3 log 5 x 3 ln x<br />
ln 5<br />
gx 6<br />
15.<br />
−9<br />
g<br />
6<br />
f<br />
9<br />
−2<br />
12<br />
g<br />
f<br />
28<br />
−6<br />
Point of intersection: 4, 3<br />
Algebraically: ln e x1 2x 5<br />
© Houghton Mifflin Company. All rights reserved.<br />
16.<br />
−8<br />
Point of intersection: 25, 6<br />
3 log 5 x 6<br />
log 5 x 2<br />
x 5 2 25 ⇒ 25, 6<br />
f x ln e x2 x 2<br />
gx 3x 2<br />
Point of intersection: 2, 4<br />
x 2 3x 2<br />
4 2x<br />
−9<br />
f<br />
g<br />
4<br />
−8<br />
9<br />
4, 3<br />
x 1 2x 5<br />
4 x<br />
x 2 ⇒ 2, 4
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