Chapter 7 Review. Name: Class: Date: = = log log log log b. 7. log log x 6 log (x + 2)
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1 Name: Class: Date: ID: A Chapter 7 Review Write the equation in logarithmic form = = 625 Evaluate the logarithm. 3. log log log 0.01 Write the expression as a single logarithm log b q + 6 log b v 7. log 3 4 log log x 6 log (x + 2) Expand the logarithmic expression. 9. log 3 d log 3 11 p log b Use the Change of Base Formula to evaluate log Use the Change of Base Formula to evaluate log Solve the exponential equation = 64 4x x = x 2 = Solve 15 2x = 36. Round to the nearest ten-thousandth. 1
2 Name: ID: A Solve the logarithmic equation. Round to the nearest ten-thousandth if necessary log 2x = Solve log(4x + 10) = log(x + 9) log x = log 4 log log x 4 = Solve log 3x + log 9 = 0. Round to the nearest hundredth if necessary. Write the expression as a single natural logarithm ln ln c ln x 2 ln c ln a 1 2 (ln b + ln c 2 ) 26. Solve ln(2x 1) = 8. Round to the nearest thousandth. 27. Solve ln 2 + ln x = 5. Round to the nearest thousandth, if necessary. 28. Solve ln x ln 6 = 0. Use natural logarithms to solve the equation. Round to the nearest thousandth e 4x 2 = e 2x + 12 = e x = e 2x = The table shows the location and magnitude of some notable earthquakes. How many times more energy was released by the earthquake in Peru than by the earthquake in Mexico? Earthquake Location Date Richter Scale Measure Italy October 31, El Salvador February 13, Afghanistan May 30, Mexico January 22, Peru June 23, The ph of a liquid is a measure of how acidic or basic it is. The concentration of hydrogen ions in a liquid is È È labeled H + + Use the formula ph = log H to find the ph level, to the nearest tenth, of a liquid with ÎÍ. ÎÍ [H + ] about
3 Name: ID: A 35. A construction explosion has an intensity I of W/m 2. Find the loudness of the sound in decibels if L = 10 log I I 0 and I o = W/m 2. Round to the nearest tenth. 36. The generation time G for a particular bacteria is the time it takes for the population to double. The t bacteria increase in population is shown by the formula G =, where t is the time period of the 3.3 log a P population increase, a is the number of bacteria at the beginning of the time period, and P is the number of bacteria at the end of the time period. If the generation time for the bacteria is 6 hours, how long will it take 8 of these bacteria to multiply into a colony of 7681 bacteria? Round to the nearest hour. 3
4 Chapter 7 Review Answer Section 1. ANS: log 2 32 = 5 PTS: 1 DIF: L2 REF: 7-3 Logarithmic Functions as Inverses TOP: 7-3 Problem 1 Writing Exponential Equations in Logarithmic Form KEY: logarithm 2. ANS: log = 4 3 PTS: 1 DIF: L3 REF: 7-3 Logarithmic Functions as Inverses TOP: 7-3 Problem 1 Writing Exponential Equations in Logarithmic Form KEY: logarithm 3. ANS: 4 PTS: 1 DIF: L3 REF: 7-3 Logarithmic Functions as Inverses TOP: 7-3 Problem 2 Evaluating a Logarithm KEY: logarithm 4. ANS: 5 PTS: 1 DIF: L2 REF: 7-3 Logarithmic Functions as Inverses TOP: 7-3 Problem 2 Evaluating a Logarithm KEY: logarithm 5. ANS: 2 PTS: 1 DIF: L4 REF: 7-3 Logarithmic Functions as Inverses TOP: 7-3 Problem 2 Evaluating a Logarithm KEY: logarithm 1
5 6. ANS: log b (q 3 v 6 ) PTS: 1 DIF: L3 REF: 7-4 Properties of Logarithms TOP: 7-4 Problem 1 Simplifying Logarithms 7. ANS: log 3 2 PTS: 1 DIF: L2 REF: 7-4 Properties of Logarithms TOP: 7-4 Problem 1 Simplifying Logarithms 8. ANS: none of these PTS: 1 DIF: L4 REF: 7-4 Properties of Logarithms TOP: 7-4 Problem 1 Simplifying Logarithms 9. ANS: log 3 d log 3 12 PTS: 1 DIF: L2 REF: 7-4 Properties of Logarithms TOP: 7-4 Problem 2 Expanding Logarithms 10. ANS: log log 3 p PTS: 1 DIF: L3 REF: 7-4 Properties of Logarithms TOP: 7-4 Problem 2 Expanding Logarithms 11. ANS: 1 2 log 57 1 b 2 log 74 b PTS: 1 DIF: L4 REF: 7-4 Properties of Logarithms TOP: 7-4 Problem 2 Expanding Logarithms 2
6 12. ANS: PTS: 1 DIF: L2 REF: 7-4 Properties of Logarithms TOP: 7-4 Problem 3 Using the Change of Base Formula KEY: Change of Base Formula 13. ANS: PTS: 1 DIF: L3 REF: 7-4 Properties of Logarithms TOP: 7-4 Problem 3 Using the Change of Base Formula KEY: Change of Base Formula 14. ANS: 7 12 PTS: 1 DIF: L4 REF: 7-5 Exponential and Logarithmic Equations TOP: 7-5 Problem 1 Solving an Exponential Equation Common Base KEY: exponential equation 15. ANS: 3 8 PTS: 1 DIF: L2 REF: 7-5 Exponential and Logarithmic Equations TOP: 7-5 Problem 1 Solving an Exponential Equation Common Base KEY: exponential equation 16. ANS: PTS: 1 DIF: L4 REF: 7-5 Exponential and Logarithmic Equations TOP: 7-5 Problem 2 Solving an Exponential Equation Different Bases KEY: exponential equation 17. ANS: PTS: 1 DIF: L3 REF: 7-5 Exponential and Logarithmic Equations TOP: 7-5 Problem 2 Solving an Exponential Equation Different Bases KEY: exponential equation 3
7 18. ANS: PTS: 1 DIF: L2 REF: 7-5 Exponential and Logarithmic Equations TOP: 7-5 Problem 5 Solving a Logarithmic Equation KEY: logarithmic equation 19. ANS: PTS: 1 DIF: L3 REF: 7-5 Exponential and Logarithmic Equations TOP: 7-5 Problem 5 Solving a Logarithmic Equation KEY: logarithmic equation 20. ANS: PTS: 1 DIF: L3 REF: 7-5 Exponential and Logarithmic Equations TOP: 7-5 Problem 6 Using Logarithmic Properties to Solve an Equation KEY: logarithmic equation 21. ANS: PTS: 1 DIF: L4 REF: 7-5 Exponential and Logarithmic Equations TOP: 7-5 Problem 6 Using Logarithmic Properties to Solve an Equation KEY: logarithmic equation 22. ANS: 0.04 PTS: 1 DIF: L3 REF: 7-5 Exponential and Logarithmic Equations TOP: 7-5 Problem 6 Using Logarithmic Properties to Solve an Equation KEY: logarithmic equation 23. ANS: ln 27c 3 PTS: 1 DIF: L3 REF: 7-6 Natural Logarithms OBJ: To evaluate and simplify natural logarithmic expressions NAT: A.3.h STA: L2.3.2 TOP: 7-6 Problem 1 Simplifying a Natural Logarithmic Expression KEY: natural logarithmic function 4
8 24. ANS: ln x 3 c 2 PTS: 1 DIF: L3 REF: 7-6 Natural Logarithms OBJ: To evaluate and simplify natural logarithmic expressions NAT: A.3.h STA: L2.3.2 TOP: 7-6 Problem 1 Simplifying a Natural Logarithmic Expression KEY: natural logarithmic function 25. ANS: ln c a 3 b PTS: 1 DIF: L4 REF: 7-6 Natural Logarithms OBJ: To evaluate and simplify natural logarithmic expressions NAT: A.3.h STA: L2.3.2 TOP: 7-6 Problem 1 Simplifying a Natural Logarithmic Expression KEY: natural logarithmic function 26. ANS: 1, PTS: 1 DIF: L3 REF: 7-6 Natural Logarithms STA: L2.3.2 TOP: 7-6 Problem 2 Solving a Natural Logarithmic Equation KEY: natural logarithmic function 27. ANS: 74.2 PTS: 1 DIF: L4 REF: 7-6 Natural Logarithms STA: L2.3.2 TOP: 7-6 Problem 2 Solving a Natural Logarithmic Equation KEY: natural logarithmic function 28. ANS: 6 PTS: 1 DIF: L4 REF: 7-6 Natural Logarithms STA: L2.3.2 TOP: 7-6 Problem 2 Solving a Natural Logarithmic Equation KEY: natural logarithmic function 29. ANS: PTS: 1 DIF: L3 REF: 7-6 Natural Logarithms STA: L2.3.2 TOP: 7-6 Problem 3 Solving an Exponential Equation DOK: DOK 3 5
9 30. ANS: PTS: 1 DIF: L3 REF: 7-6 Natural Logarithms STA: L2.3.2 TOP: 7-6 Problem 3 Solving an Exponential Equation DOK: DOK ANS: PTS: 1 DIF: L2 REF: 7-6 Natural Logarithms STA: L2.3.2 TOP: 7-6 Problem 3 Solving an Exponential Equation 32. ANS: PTS: 1 DIF: L2 REF: 7-6 Natural Logarithms STA: L2.3.2 TOP: 7-6 Problem 3 Solving an Exponential Equation 33. ANS: about 5.48 times as much energy PTS: 1 DIF: L3 REF: 7-3 Logarithmic Functions as Inverses TOP: 7-3 Problem 3 Using a Logarithmic Scale KEY: logarithm logarithmic scale DOK: DOK ANS: 2.2 PTS: 1 DIF: L4 REF: 7-3 Logarithmic Functions as Inverses TOP: 7-3 Problem 3 Using a Logarithmic Scale KEY: logarithm problem solving 35. ANS: decibels PTS: 1 DIF: L3 REF: 7-4 Properties of Logarithms TOP: 7-4 Problem 4 Using a Logarithmic Scale 6
10 36. ANS: 85 hours PTS: 1 DIF: L4 REF: 7-5 Exponential and Logarithmic Equations TOP: 7-5 Problem 4 Modeling With an Exponential Equation KEY: logarithmic equation DOK: DOK 3 7
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