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Plug it in and round to three decimal places. 17. e3 18.  EMBED Equation.DSMT4  19. ln 1.6 20. 4ln 6 + 7 21. 5ln 7 ln 8 Part 3: Expand the expression using the properties of logs. The word log will be used repeatedly in each problem. 1. log6 3x 2. log2  EMBED Equation  3. log10 xy2 4. log4  EMBED Equation  5. log5 2 EMBED Equation  6.  EMBED Equation.DSMT4  7. ln x1/2yz 8. ln 5x3 9.  EMBED Equation.DSMT4  Part 4: Condense the expression using the properties of logs. The word log will be used once in each problem. 1. log3 8 - log3 2 2. 2 log5 4 + log5 3 3. log4 5 + log4 3 + log4 1 4.  EMBED Equation  log10 24 log10 4 5.  EMBED Equation  log2 x 3 log2 y 6. log3 4 + 2 log3 x log3 5 7.  EMBED Equation log2 x 2 logs y 8. 3loga 2 +  EMBED Equation loga 27 -  EMBED Equation loga 16 9. ln x + ln 5 10. ln 4 ln y 11. 4 ln x + 5 ln y 12. ln 6 (ln x + ln 3) 13. ln 4 + 3 ln x + ln y Part 5: Solve for x. If x is the argument of the log, then change each problem to exponential form & solve 1. log6 x = 2 2. log5 x = 3 3. log16 x =  EMBED Equation  4. log9 x =  EMBED Equation  5. log2 x = -1 6. log7 x = 3 7. log4 4(x+2) = 5 8. log3 x = 4 Part 6: Change Base Solve for x. Round to 3 decimal places if necessary. If x is the exponent of the log, then use the change base formula and the calculator. Be sure to get the exponent by itself! 1. log3 5 = x 2. log 6 50 = x 3. log 3 15 = x 4. 10x = 200 5. 7x = 300 6. 5x - 6 = 100 7. 16 4x = 10 8. 5x = 12 9. 5 x + 2 = 500 10. 2x = 1,000,000 11.  EMBED Equation.DSMT4  12. 5(1.5) x = 3000 13. 8x 4 = 75 14. 48 2x = 40 15. 6(1.2)x = 18 16.  EMBED Equation  18.  EMBED Equation  19.  EMBED Equation  20.  EMBED Equation  21.  EMBED Equation  Part 7: Condense & Solve Condense the each side of the equation, then solve for x. If there is a log with the same base on both sides then they cancel. 1. log5 x = 3 log5 2 2. log 4 x = log 4 15 log 4 3 3.  EMBED Equation  4.  EMBED Equation  5.  EMBED Equation  6.  EMBED Equation  7.  EMBED Equation  8.  EMBED Equation  9.  EMBED Equation  10.  EMBED Equation  11. 2 log4 3 = log4 x 12. log10 x + log 10 3 = log10 12 13. log3 5 log3 x = log3 2 14.  EMBED Equation log3 16 = log3 x 15.  EMBED Equation log10 x = log10 3 16. 3 log5 2 + log5 x = log5 24 17. ln x = 2 ln 3 18.  EMBED Equation  19.  EMBED Equation  20.  EMBED Equation  Part 8: Applications Write the equation and solve each problem. 1. The population of bacteria can be represented by the formula N = Noekt, where No is the initial number of bacteria in the culture. N is the number after t hours, and k is a constant determined by the type of bacteria and the conditions. When will a culture of 300 bacteria, where k = 0.068, reach a count of 10,000? 2. A college math class consists of 32 students. On Monday at 9 AM, the teacher tells one student to notify the others that the test scheduled for Wednesday at 9 AM has been cancelled. The model for the number of students in the class who have heard this information after t hours is N = 32 32e-0.02t. After how many hours will half of the class have been notified? 3. The power of supply of a satellite decreases exponentially over the time it is being used. The equation for determining the power supply P, in watts, after t days is P =  EMBED Equation.DSMT4 . Determine the number of days it will take for the power supply to be less than 30W. 4. A fossil contains 47 mg of carbon-14. Using the carbon-14 formula, A =  EMBED Equation.DSMT4 , determine the age of the fossil if it originally contained 93 mg of carbon-14. 5. Mr. Campbell invested $6500 in an account paying 6.5% interest compounded continuously. How long to the nearest year will it take the money in the account to increase by $1500? A = Pert 6. $500 is invested at 6% annual interest, compounded quarterly. When will the balance double?  EMBED Equation.DSMT4  7. 2000 is invested at 7% annual interest, compounded monthly. When will the balance triple?  EMBED Equation.DSMT4  8. A population of 450 animals decreases at an annual rate of 16% per year. How long before there are only 100 animals left? 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