IAT SOLUTIONS - C_7.pdf

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Chapter 7, continuedlog (100h)b. s(h) 5 2 ln (100h) 5 2 1}log e 2 5 2} p log (100h)log e25 }log e (log 100 1 log h) 5 2} (2 1 log h)log eMixed Review75.F 5 2812 20G F 1 6 722 219G F 5 11 2110 1G27 1176.F6 3G F 2 29 17213 1G F 5 2 2619 2G1.7 2.4 6.877. 3F9.2 5.3 7.2G F 5 5.1 7.2 20.427.6 15.9 21.6G78. Ï } x 1 12 1 4 5 11 79. Ï 3} x 1 10 1 6 5 4Ï } x 1 12 5 73Ï } x 1 10 5 22Check:x 1 12 5 49 x 1 10 5 28Ï } x 1 12 1 4 5 11Ï } 37 1 12 1 4 0 11x 5 37 x 5 218Ï } 49 1 4 0 11Check:3Ï } x 1 10 1 6 5 43Ï } 218 1 10 1 6 0 43Ï } 28 1 6 0 47 1 4 0 11 22 1 6 0 411 5 11 ✓ 4 5 4 ✓37 is the solution. 218 is the solution.80. Ï } x 1 6 5 Ï } 3x 2 14 81. 3 Ï } 2x 2 7 5 3 Ï } 8 2 xx 1 6 5 3x 2 142x 2 7 5 8 2 x22x 5 220 3x 5 15x 5 10 x 5 5Check:Check:Ï } x 1 6 5 Ï } 3x 2 143Ï } 2x 2 7 5 Ï 3} 8 2 xÏ } 10 1 6 0 Ï } 3(10) 2 143Ï } 2(5) 2 7 0 Ï 3} 8 2 5Ï } 16 0 Ï } 30 2 143Ï } 10 2 7 0 Ï 3 } 3Ï } 16 5 Ï } 16 ✓3Ï } 3 5 Ï 3 } 3 ✓10 is the solution. 5 is the solution.82. Ï } x 2 1 5 x 2 3x 2 1 5 x 2 2 6x 1 90 5 x 2 2 7x 1 100 5 (x 2 5)(x 2 2)x 5 5 or x 5 2Check x 5 5: Check x 5 2:Ï } 5 2 1 0 5 2 3 Ï } 2 2 1 0 2 2 3Ï } 4 0 2 Ï } 1 0 212 5 2 ✓ 1 Þ 212 is an extraneous solution, so the 5 is the only solution.83. x 1 2 5 Ï } 9x 1 28x 2 1 4x 1 4 5 9x 1 28x 2 2 5x 2 24 5 0(x 2 8)(x 1 3) 5 0x 5 8 or x 5 23Check x 5 8: Check x 5 238 1 2 0 Ï } 9 p 8 1 28 23 1 2 0Ï } 9(23) 1 2810 0 Ï } 100 21 0 Ï } 110 5 10 ✓ 21 Þ 123 is an extraneous solution, so 8 is the only solution.84. e 8 ø 2981 85. e 26 ø 0.0024886. e 3.5 ø 33.12 87. e 20.4 ø 0.67088. log 12 ø 1.079 89. log 1.8 ø 0.25590. ln 24 ø 3.178 91. ln 8.49 ø 2.139Quiz 7.4 – 7.5 (p. 513)1. 4 2 5 16, so log 416 5 2 2. 5 0 5 1, so log 51 5 03. 8 1 5 8, so log 88 5 14. 1 }1 22 25 5 32, so log 1/232 5 255.7.211yx6.y(1, 2)y 5 ln x 1 2(2, 2.69)1(2, 0.69)21 (1, 0)y 5 ln xDomain: x > 0 Domain: x > 0Range: all real numbersy(9, 2)2(3, 1)(21, 0) (5, 1)24 (1, 0)(23, 21)y 5 log 3 (x 1 4) 2 1Domain: x > 24y 5 log 3 xRange: all real numbers8. log 25x 5 log 25 1 log 2x9. log 5x 7 5 7log 5xxRange: all real numbers10. ln 5xy 3 5 ln 5 1 ln x 1 ln y 3 5 ln 5 1 ln x 1 3 ln y11. log 36y 4}x 8 5 log 3 6y4 2 log 3x 85 log 36 1 log 3y 4 2 log 3x 85 log 36 1 4 log 3y 2 8 log 3x512. log 35 2 log 320 5 log 3 }20 5 log 1}3 413. ln 6 1 ln 4x 5 ln 6 p 4x 5 ln 24x14. log 65 1 3 log 62 5 log 65 1 log 62 35 log 65 1 log 68 5 log 68 p 55 log 640xCopyright © by McDougal Littell, a division of Houghton Mifflin Company.438Algebra 2Worked-Out Solution Key
Chapter 7, continued15. 4 ln x 2 5 ln x 5 ln x 4 2 ln x 5 5 ln }x4x 5 ln 1 5 } xlog 1016. log 310 5 }log 3 ø 1}0.4771 ø 2.096log 1417. log 714 5 }log 7 ø }1.14610.8451 ø 1.356log 2418. log 524 5 }log 5 ø }1.38020.6990 ø 1.975log 4019. log 840 5 }log 8 ø }1.60210.9031 ø 1.77420. I 5 10 24 W/m 2 ; I 05 10 212 W/m 2L(I ) 5 10 log1 I }I 02 5 10 log 1 }102410 212 25 10 log 10 8 5 10 p 8 5 80The alarm clock’s loudness is 80 decibels.Graphing Calculator Activity 7.5 (p. 514)1. 2.3. 4.13. The natural log, or ln x, is equal to log ex. So, if you didnot have a natural logarithm then you could graphy 5 ln x by graphing y 5 }log xlog e .Lesson 7.67.6 Guided Practice (pp. 515 – 519)1. 9 2x 5 27 x 2 1 2. 100 7x 1 1 5 1000 3x 2 2(3 2 ) 2x 5 (3 3 ) x 2 1 (10 2 ) 7x 1 1 5 (10 3 ) 3x 2 23 4x 5 3 3x 2 3 10 14x 1 2 5 10 9x 2 64x 5 3x 2 3 14x 1 2 5 9x 2 6x 5 23 5x 5 283. 81 3 2 x 5 1 }1 32 5x 2 6 4. 2 x 5 5x 5 2 8 }5(3 4 ) 3 2 x 5 (3 21 ) 5x 2 6 log 22 x 5 log 253 12 2 4x 5 3 25x 1 6 x 5 log 2512 2 4x 5 25x 1 6 x 5 log5 }log2 ø 2.32x 5 265. 7 9x 5 15 6. 4e 20.3x 2 7 5 13log 77 9x 5 log 715 4e 20.3x 5 209x 5 log 715 e 20.3x 5 5x 5 log15 }9log7 ø 0.15 ln e20.3x 5 ln 520.3x ø 1.6094Copyright © by McDougal Littell, a division of Houghton Mifflin Company.5. 6.7. 8.9. 10.11. 12.x ø 25.367. ln (7x 2 4) 5 ln (2x 1 11)7x 2 4 5 2x 1 115x 5 15x 5 3Check: ln (7x 2 4) 5 ln (2x 1 11)ln (7 p 3 2 4) 0 ln (2 p 3 1 11)ln 17 5 ln 17 ✓8. log 2(x 2 6) 5 52 log 2 (x 2 6) 5 2 5x 2 6 5 32x 5 38Check: log 2(x 2 6) 5 log 2(38 2 6) 5 log 232Because 2 5 5 32, log 232 5 5. ✓9. log 5x 1 log (x 2 1) 5 2log [5x(x 2 1)] 5 210 log[5x(x 2 1)] 5 10 25x(x 2 1) 5 1005x 2 2 5x 2 100 5 0x 2 2 x 2 20 5 0(x 2 5)(x 1 4) 5 0x 5 5 or x 5 24Algebra 2Worked-Out Solution Key439
Page 1 and 2: Chapter 7Copyright © by McDougal L
Page 4 and 5: Chapter 7, continued37. A 5 2200 1
Page 6 and 7: Chapter 7, continued5.y(0, 5)10( 1,
Page 8 and 9: Chapter 7, continuedb. When t 5 50:
Page 10 and 11: Chapter 7, continued11. Amount of i
Page 12 and 13: Chapter 7, continuedd. P(2.75) 5 30
Page 14 and 15: Chapter 7, continued11. 2 6 5 64, s
Page 16 and 17: Chapter 7, continued72. x 1/2 p x 2
Page 18 and 19: Chapter 7, continuedlog 1732. When
Page 22 and 23: Chapter 7, continuedCheck: log 5x 1
Page 24 and 25: Chapter 7, continued31. log 8(5 2 1
Page 26 and 27: Chapter 7, continued43. log 3(x 2 9
Page 28 and 29: Chapter 7, continued57. When R 5 5:
Page 30 and 31: Chapter 7, continued70. f(1) f(2) f
Page 32 and 33: Chapter 7, continued10. 2 log 4x 2
Page 34 and 35: Chapter 7, continued2. You can dete
Page 36 and 37: Chapter 7, continued17. (2, 3): 3 5
Page 38 and 39: Chapter 7, continued28. The express
Page 40 and 41: Chapter 7, continued40. y 5 kx when
Page 42 and 43: Chapter 7, continued14. (3, 12): 12
Page 44 and 45: Chapter 7, continued14.y 5 e x(1, 2
Page 46 and 47: Chapter 7, continued3.f(x) 5 25 ? 2
Page 48 and 49: Chapter 7, continued8. D; y 5 2(0.5

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