IAT SOLUTIONS - C_7.pdf

Chapter 7, continuedCopyright © by McDougal Littell, a division of Houghton Mifflin Company.7. a.Oil collected(billions of barrels)y60504030201000 500 1000 1500 2000 2500 xWells drilledb. Using the graph, you can estimate that you couldexpect to collect about 40 billion barrels after drilling1000 wells.c. Using the graph, you can estimate that about 2400wells need to be drilled in order to collect 50 billionbarrels of oil.Lesson 7.57.5 Guided Practice (pp. 507–509)1. log6 }5 8 5 log 6 5 2 log 8 ø 0.898 2 1.161 5 20.26362. log 640 5 log 6(8 p 5) 5 log 68 1 log 65ø 1.161 1 0.898 5 2.0593. log 664 5 log 68 2 5 2log 68 ø 2(1.161) 5 2.3224. log 6125 5 log 65 3 5 3log 65 ø 3(0.898) 5 2.6945. log 3x 4 5 log 3 1 log x 4 5 log 3 1 4log x6. ln 4 1 3 ln 3 2 ln 12 5 ln 4 1 ln 3 3 2 ln 125 ln 4 1 ln 27 2 ln 125 ln }4 p 27 5 ln }10812 12 5 ln 97. log 58 5 }log 8log 5 ø }0.90310.6990 ø 1.292log 148. log 814 5 }log 8 ø }1.14610.9031 ø 1.2699. log 269 5 }log 9log 26 ø }0.95421.4150 ø 0.674log 3010. log 1230 5 }log 12 ø }1.47711.0792 ø 1.36911. Increase in loudness 5 L(3I ) 2 L(I )5 10 log }3I 2 10 log }I I 0I 05 10 1 log 3I }I 02 log I }I 025 10 1 log 3 1 log I }I 02 log I }I 025 10(log 3) ø 4.8The loudness increases by about 4.8 decibels.7.5 Exercises (pp. 510 – 513)Skill Practice1. To condense the expression log 32x 1 log 3y, youneed to use the product property of logarithms.2. You can evaluate log 712 by using thechange-of-base formula with common logarithmsor with natural logarithms, and then using acalculator to evaluate the result.3. B; ln 6 2 ln 2 5 ln 6 }2 5 ln 34. D; 2 ln 6 5 ln 6 2 5 ln 365. A; 6 ln 2 5 ln 2 6 5 ln 646. C; ln 6 1 ln 2 5 ln 6 p 2 5 ln 127. log 3 5 log }12 5 log 12 2 log 44ø 1.079 2 0.602 5 0.4778. log 48 5 log 12 p 4 5 log 12 1 log 4ø 1.079 2 0.602 5 1.6819. log 16 5 log 4 2 5 2 log 4 ø 2(0.602) 5 1.20410. log 64 5 log 4 3 5 3 log 4 ø 3(0.602) 5 1.80611. log 144 5 log 12 2 5 2 log 12 ø 2(1.079) 5 2.15812. log }1 3 5 log }4 5 log 4 2 log 1212ø 0.602 2 1.079 5 20.47713. log }1 5 log 1 2 log 4 ø 0 2 0.602 5 20.602414. log }1 5 log 1 2 log 12 ø 0 2 1.079 5 21.0791215. log 34x 5 log 34 1 log 3x16. ln 15x 5 ln 15 1 ln x17. log 3x 4 5 log 3 1 log x 4 5 log 3 1 4 log x18. log 5x 5 5 5 log 5x19. log 22 }5 5 log 2 2 2 log 2 520. ln }12 5 ln 12 2 ln 5521. log 4x }3y 5 log 4 x 2 log 4 3y 5 log 4 x 2 log 4 3 2 log 4 y22. ln 4x 2 y 5 ln 4 1 ln x 2 1 ln y 5 ln 4 1 2 ln x 1 ln y23. log 75x 3 yz 2 5 log 75 1 log 7x 3 1 log 7y 1 log 7z 25 log 75 1 3 log 7x 1 log 7y 1 2 log 7z24. log 636x 2 5 log 636 1 log 6x 2 5 log 636 1 2 log 6x25. ln x 2 y 1/3 5 ln x 2 1 ln y 1/3 5 2 ln x 1 1 }3 ln y26. log 10x 3 5 log 10 1 log x 3 5 log 10 1 3 log x27. log 2Ï } x 5 log 2x 1/2 5 1 }2 log 2 x28. ln }6x2y 5 ln 4 6x2 2 ln y 4 5 ln 6 1 ln x 2 2 ln y 45 ln 6 1 2 ln x 2 4 ln y29. ln 4 Ï } x 3 5 ln x 3/4 5 3 }4 ln x30. log 3Ï } 9x 5 log 33 Ï } x 5 log 33x 1/2 5 log 33 1 log 3x 1/25 log 33 1 1 }2 log 3 x31. When expanding the logarithmic expression, thequantities (log 25) and (log 2x) should have been added,not multiplied.log 25x 5 log 25 1 log 2xAlgebra 2Worked-Out Solution Key435