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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 .
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2. Graph f ( x) = e− x − 4 .
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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
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5. Use the property of logarithms to expand the logarithmic expressions.
4 x3
log
y
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6. Use the property of logarithms to condense the logarithmic expression.
3[log6 x + log6 7]
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7. Convert the exponential expression to logarithmic form. 12 x = 450
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8. Convert the logarithmic expression to exponential form. ln 12 ≈ 2.485
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9. Solve the equation for x. Round your answer to two decimals.
log 4 x = 3
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10. Solve the equation for x. Round your answer to two decimals.
e x +3 = 12
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11. Solve the equation for x. Round your answer to two decimals.
log 9 x − log 9 12 = 2
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12. Solve the equation for x. Round your answer to two decimals.
log 3 x + log 3 7 = log 3 50
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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 + ])