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Advanced Algebra Ch. 8 Name___________________
Review Worksheet
Non Calculator Part (Problems 1-32)
Write an equivalent exponential or logarithmic function.
3 5 = 125 2.
3
16 4 = 8 3. ln x = 6 4. log 1 7 = 0
x e = 7 6. (^9)
log 2 81
5 e = x 8. ln 8 =x
Write the expression as a sum or difference of logarithms or multiples of logarithms.
2 3 log 5x 6 y 10.
5
3
xy ln z
Write the expression as a single logarithm.
2 ln y ln x 3
- 2 log 2 x + 3log b 2 โ log 2 y โ4 log a 2
Evaluate without a calculator.
- log 32 2 14.
4 log 6 6
log 27
- log 64 8
Solve each equation. Check your solutions.
4x 1 2x 9 3 3
โ โ = 18.
(^1) x 6 5 25
=
2x 5 4x 1 8 16
y 5y 3 1 9 27
โ ๏ฃซ^ ๏ฃถ
- (^) b
log 3 64
2 log 12 x โ 7 = log 12 x + 5
2 6 6
log 2b + 1 = log 6 โ 9b 24. a
log 32 2
log x log 8 3
= 26. log 2 3 +^ log^3 ( y^ +^4 )^ =log 6 3
Solve the equations. Round to the nearest ten-thousandth
x 2 = 27 40.
x 2 x 7 5
โ = 41.
2x 3 3x 2 3
=
- After 12 hours, half of a 16-gram sample of radioactive element is left. What is the approximate
value of k in the formula
kt y = Ce? Assume t is measures in hours. Round your answer to four decimal
places.
- For a certain strain of bacteria, k is 0.728 when t is measured in days. How long will it take 10
bacteria to increase to 675 bacteria?
- Carl plans to invest $500 at 8.25% interest, compounded continuously. How long will it take for his
money to triple? Round your answer to the nearest tenth of a year.
rt Use the formula A =Pe.
Answers to Ch. 8 Review Worksheet:
- log 125 5 = 3 2. 16
log 8 4
6 e = x 4.
0 7 = 1 5. (^) x =ln 7
โ = 7. ln x = 5 8.
x e = 8 9. (^6 6 )
log 5 2 log x log y 2
- ln x + 5ln y โ 3ln z 11.
2 3 ln y x 12.
2 3
(^2 )
x b log ya
- (^) x = โ 4 18. (^) x = โ 8
x 10
y 13
= 21. b = 4 22. x = 4, โ 3
b , 5 2
= โ 24. a = 4 25. x = 2 26. y = โ 1 27. x = 3
- x = 4 29.
x 2
= 30. x = 6 31. a = 44 32. y = 6
- 5.8 days 44. 13.3 years
