524 CHAPTER 4 Inverse, Exponential, and Logarithmic Functions 4. (a) Write 43/2 = 8 in logarithmic form. (b) Write log8 4 = 2 3 in exponential form. 5. Graph ƒ1x2 = A1 2B x and g1x2 = log1/2 x on the same axes. What is their relationship? 6. Use properties of logarithms to rewrite the expression. Assume all variables represent positive real numbers. log7 x224 y z3 Use a calculator to find an approximation to four decimal places for each logarithm. 7. log 2388 8. ln 2388 9. log9 13 Solve each equation. Give irrational solutions as decimals correct to the nearest thousandth. 10. 12x = 1 11. 162x+1 = 83x 12. 9x = 4 13. 2x+1 = 3x-4 14. e0.4x = 4x-2 Solve each equation. Give solutions in exact form. 15. x2/3 = 25 16. 2e2x - 5ex + 3 = 0 17. logx 9 16 = 2 18. log2 31x - 421x - 224 = 3 19. log2 x + log2 1x + 22 = 3 20. ln x - 4 ln 3 = ln 1 5 x 21. log3 1x + 12 - log3 1x - 32 = 2 22. A friend is taking another mathematics course and says, “I have no idea what an expression like log5 27 really means.” Write an explanation of what it means, and tell how we can find an approximation for it with a calculator. Solve each problem. 23. (Modeling) Skydiver Fall Speed A skydiver in free fall travels at a speed modeled by v1t2 = 17611 - e-0.18t2 feet per second after t seconds. How long, to the nearest second, will it take for the skydiver to attain a speed of 147 ft per sec 1100 mph2? 24. Growth of an Account How many years, to the nearest tenth, will be needed for $5000 to increase to $18,000 at 3.0% annual interest compounded (a) monthly and (b) continuously? 25. Tripling Time For any amount of money invested at 2.8% annual interest compounded continuously, how long, to the nearest tenth of a year, will it take to triple? 26. (Modeling) Radioactive Decay The amount of a certain radioactive material, in grams, present after t days is modeled by A1t2 = 600e-0.05t. (a) Find the amount present after 12 days, to the nearest tenth of a gram. (b) Find the half-life of the material, to the nearest tenth of a day.
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