Walden Univ Change the Equations from Exponential Form to Logarithmic Form Ques

Mathematics

Walden University

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DESK Pre-Calculus 12 Unit 4 Send-In Assignment On-Line Course SEND - IN ASSIGNMENT UNIT 4 Exponents & Logarithms Name: _________________________________________ Teacher:________________________________________ If you are cross enrolled, state your other school besides DESK. _________________________________________ Date that you submitted this assignment: _________________________________________  To receive full credit for your answers to the questions, show ALL work. Total ______ = _________% 58 2017 Page 1 of 9 Unit 4 DESK Pre-Calculus 12 Unit 4 Send-In Assignment On-Line Course All answers rounded to 2 decimal places unless otherwise stated. 1. Solve the following for x algebraically. Verify your solution. a) 4−2𝑥+1 = 8𝑥−4 a) _____________________________ 2 marks 1 b) 92𝑥−1 = ( ) 27 𝑥+2 b) _____________________________ 2 marks c) 4 𝑥 2 −𝑥 =1 c) _____________________________ 2 marks d) log 3𝑥 36 = 2 d) _____________________________ 2 marks 2017 Page 2 of 9 Unit 4 DESK Pre-Calculus 12 Unit 4 Send-In Assignment On-Line Course Evaluate: log 6 58 using the change of base rule. 2. 2. _____________________________ 1 mark 3. Change each of the following from exponential form to logarithmic form. a) 0.2𝑦 = 5(7)𝑥 a) _____________________________ 2 marks b) 72𝑥−1 = 17𝑥 b) _____________________________ 3 marks 4. Change each of the following from logarithmic form to exponential form 𝑦 = 𝑎𝑏 𝑥 𝑦 a) log 3 5 = 𝑥 a) _____________________________ 1 mark 2017 Page 3 of 9 Unit 4 DESK Pre-Calculus 12 Unit 4 Send-In Assignment On-Line Course b) log10 (0.5𝑦) = 𝑥 b) _____________________________ 1 mark 5. Solve the following for x. State in log form AND as a numerical value rounded to the nearest hundredth. (3 marks each) a) 65𝑥+1 = 4𝑥 b) 7(5)𝑥 = 8𝑥+1 2017 Page 4 of 9 Unit 4 DESK Pre-Calculus 12 Unit 4 Send-In Assignment On-Line Course 6. Evaluate the following using the laws of logarithms without a calculator. a) log 5 10 + log 5 75 − (log 5 2 + log 5 3) a) _____________________________ 2 marks 1.5 b) log 5 625 b) _____________________________ 2 marks 7. Write each expression as a single logarithm. 1 a) 5 log 𝑥 − 2 log 𝑦 − 3 log 𝑧 a) _____________________________ 2 marks b) 3 4 log 𝑎 𝑏 + 4 log 𝑎 𝑐 − 3 log 𝑎 𝑏 b) _____________________________ 2 marks 2017 Page 5 of 9 Unit 4 DESK Pre-Calculus 12 Unit 4 Send-In Assignment On-Line Course 8. Solve for x algebraically. Verify your solutions. a) log 5 𝑥 − log 5 (𝑥 − 1) = log 5 3 a) _____________________________ 3 marks b) log 4 (𝑥 − 5) + log 4 (𝑥 − 2) = 1 b) _____________________________ 3 marks 2 c) log 𝑥 = 3 log 27 + 2 log 2 − log 3 c) _____________________________ 3 marks 2017 Page 6 of 9 Unit 4 DESK Pre-Calculus 12 Unit 4 Send-In Assignment On-Line Course d) 2 log 3 𝑥 − log 3 2𝑥 = 2 d) _____________________________ 3 marks 9. If log 3 = 𝑎 and log 8 = 𝑏, determine log 18 in terms of a and b. 9. _____________________________ 2 marks 𝑥+1 10. Graph 𝑦 = 2 − 4. Indicate the asymptote with a dotted line. Clearly show at least four points on the graph (include the intercepts). Use the space to show how you calculated the coordinates. 5 5 5 5 4 marks 2017 Page 7 of 9 Unit 4 DESK Pre-Calculus 12 Unit 4 Send-In Assignment On-Line Course 11. If you invest $800 at 7.5% compounded annually, how many years (to the nearest tenth) would it take for your investment to grow to $2000? 11. _____________________________ 2 marks 12. A colony of bees increases by 35% every four months. How many bees should a beekeeper start with if she wishes to have 10,000 bees in 18 months? 12. _____________________________ 2 marks 13. An archeologist finds a fossil that contains 60 milligrams of carbon-14. She knows that the bone originally contained 100 milligrams of carbon-14. How old is the fossil if the half-life of carbon-14 is 5,700 years? 13. _____________________________ 2 marks 2017 Page 8 of 9 Unit 4 DESK Pre-Calculus 12 Unit 4 Send-In Assignment On-Line Course 14. A major earthquake of magnitude 8.7 is 150 times as intense as a minor earthquake. Determine the magnitude, to the nearest tenth, of the minor earthquake. 14. _____________________________ 2 marks 15. Determine the inverse function of 𝑓(𝑥) = 5𝑥−7 + 3 15. _____________________________ 2 marks 2017 Page 9 of 9 Unit 4 ...
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