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NAME:_________________________________________ PRECALCULUS HONORS CHAPTER 3 REVIEW – EXPONENTIAL AND LOGARITHMIC FUNCTIONS QUESTIONS #1-11 SHOULD BE COMPLETED WITHOUT THE USE OF ANY CALCULATOR!!! 1. Find the solution to the equation ln (x2 + 3x ) ln 10 = 0 . a) x = 5 or x = 2 b) x = 5 or x = 2 c) x = 5 d) x = 2 2. Find the solution to the equation log x 8 1 . 3 a) x = 512 b) x = 24 c) x 1 d) x = 2 c) 3 d) 0 8 3. Solve for x log 8 x 3 . 3 2 27 a) 6 4. b) 3 The range for a logarithmic function is ______________? a) all real numbers 5. c) y > 0 d) all rational numbers Express as a single logarithm 5 log 3 x . 3 3 5 b) log 3 x a) log3 x 5 6. b) x > 0 3 Solve for x log 2 (x + 7) + log 2 x = 3 . a) x 7 3 b) 1 c) log3 3 x5 d) log 3 x5 3 c) not possible d) none of these c) not possible d) none of these c) 2 d) 4 x x 7. Evaluate log 1 3 1 . 3 a) x b) 1 3 x 8. What is the solution of 1 7 x 4 ? 7 a) 2 9. b) 0 Find the approximate value of the expression log 16 160 . a) 0.54 b) 1.83 c) 2.20 10. Find the value of the expression eln2.5 . a) 30 b) 12.2 c) 2.5 d) 10 d) 0.9 11. Which of the following is not an exponential function. a) f(x) = 5(2.7)x b) f(x) = 7x2 c) f(n) = 125e0.12n d) f(x) = 6.5 3 4 x YOU MAY USE A CALCULATOR TO SOLVE QUESTIONS #1215. SHOW ALL WORK!!! 12. Janet deposited $3200 at 4.5% annual interest, compounded quarterly. How long will it take this money to triple in value? 13. Find the approximate solution(s) to the equation: 3(1.5) x + 10 = 280. 14. Find the solution(s) to the equation: 2 log a 3 + log a (x – 4) = log a (x + 8) . Solve the following problem. Round your answer to the nearest tenth. Show all your work. 15. The amount of pollutant, measured in parts per million, in Pine Lake can be modeled by the function A(t) = 14e0.16t , where t is the number of years since a program began to clean up the lake. Approximately how long will it take for the amount of pollutant in Pine Lake to reach 7 parts per million? SKETCH THE FOLLOWING FUNCTIONS – NO CALCULATORS!!! f ( x) 32 x 1 x 1 17. g ( x) 2 3 18. h( x) 2log 4 (3 x) 1 19. i ( x) log 2 ( x 2) 4 16. Be sure to review your homework problems, the worksheets on solving exponential and log equations. Know how to use the change of base formula to simplify and evaluate log expressions without a calculator, and know your properties of logs and exponents insideout.