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College Algebra Unit 5 Test Practice Test Name: ____________________________________ Period: _________ Date: _____________________ Directions: Choose the best answer choice for each question. _______ 1. Describe the transformations on the parent function of f ( x) = −2 x + 1 . _______ 2. Graph f ( x) = e− x − 4 . _______ 3. Robert invests $12,000 in an account which has an annual interest rate of 4.5%. If interest is compounded quarterly, how much money will be in the account after 10 years? _______ 4. What is the value of the logarithm? log121 11 _______ 5. Use the property of logarithms to expand the logarithmic expressions. 4 x3 log y _______ 6. Use the property of logarithms to condense the logarithmic expression. 3[log6 x + log6 7] ______ 7. Convert the exponential expression to logarithmic form. 12 x = 450 ______ 8. Convert the logarithmic expression to exponential form. ln 12 ≈ 2.485 _______ 9. Solve the equation for x. Round your answer to two decimals. log 4 x = 3 _______ 10. Solve the equation for x. Round your answer to two decimals. e x +3 = 12 _______ 11. Solve the equation for x. Round your answer to two decimals. log 9 x − log 9 12 = 2 _______ 12. Solve the equation for x. Round your answer to two decimals. log 3 x + log 3 7 = log 3 50 _______ 13. Sherry bought a house for $100,000. Her loan has an interest rate of 3.3% and interest is compounded monthly. If she does not pay a single payment, how long will it take for her loan to double to $200,000? Extended Response: 14. Graph f ( x) = −3 x + 2 15. Bobby invests $8,000 in the bank. He receives an interest rate of 3.6% and interest is compounded continuously. If the account is left untouched, how much money will be in the account after 12 years? For problems 16 and 17, use the property of logarithms to expand the logarithmic expressions. 16. log 2 73 x 5 17. log 7 y 3z 4 For problem 18, use the property of logarithms to condense the logarithmic expressions. 18. log8 4 + log 8 x − log 8 y For problems 19 and 20, use the property of logarithms and the given information to approximate the value of each logarithm. Given: logb 2 = 3.5 , logb 3 = 4 , and logb 5 = 4.7 19. log b 18 20. log b 6 5 For problems 21-24, solve the equation for x. Round your answer to two decimals. 21. 2(3 x ) − 5 = 157 22. log 2 ( x − 5) = 4 23. log 2 3 + log 2 ( x −1) = 2 24. 6 2 x +3 = 6 5 x −1 25. Find the pH level of green tea if it has a hydrogen ion concentration of 8 ×10 −10 . Is green tea neutral, acidic or basic? (Remember pH = − log[ H + ])