Unit 11 Review
Name ______________________________________ Date _______________ Period _______
Unit 11 Review
– Logarithms
Review.
1. Solve 3(6x -1)
² = 48
2. List the equations in order from widest to narrowest graph. y = -3x ², y = 0.3x², y = 5x², y = -0.5x²
3. Find the equation of the line that passes through the points (-5, -4) and (7, 5).
Expand each logarithmic expression.
4. log
3 a
5 b
3
______________________________
2 x
5. log
3
5
6. log
3
6 ab
4 ab
3
7. log
3 c
4
Condense each logarithmic expression.
8.
1
2 log
2
5
 log
2
M
9. log
3
4

2 log
3 x
10. 5 log a

2 log b

3 log c
______________________________
______________________________
_____________________________
____________________
____________________
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Evaluate. Write down what you put into the calculator. Round to 4 decimal places.
11. log
5
9 ____________________
12. log
12
2 ____________________

Unit 11 Review
Solve each equation. Show all steps/work. Round to 4 decimal places, where necessary.
13. log
5 m

3
14. 4 x 
80
15. log
2 x

3 log
2
2

2 log
2
10 16. log
3 x
 log
3
3
 log
3
12
17. log
2 x

3
19. 5 ( 3
2 x
)

6

49
18.
20.
3 (log log
4
(
4 x
3 x

 log
4
1 )

8 log
)
4

(
9
2 x

3 )

Unit 11 Review
Use the following formulas to solve the word problems. A

P


1 r n


 nt
N

N
0


1
2

 h t
21. If you deposit $5000 in an account that pays 4.5% compounded monthly, how much would you have in 2 years? Round answer to nearest $100.
22. One isotope of Chromium has a half-life of 50 days. How long would it take for 1000 g to decay to 50 grams? (3 decimal places)
23. If you deposited $4000 into an account that pays 9.5% compounded quarterly, how long would it be before you had $15,000? (3 decimal places)
24. How much of a 300 kg sample of Californium with a half-life of 45 hours would be left after 3 days? (3 decimal places)
25. If 60 kg of a 162 kg sample of a radioactive isotope will remain after 13 hours, calculate the half-life of the radioactive isotope to the nearest hour.

Answers
1.
5

,
6 2
1
2. y = 0.3x
², y = -0.5 x², y = -3x², y = 5x²
3.
4. y

3
4
5 log
3 x a

1

4
3 log
3 b
5. log
3
6. log
3
7. log
3
2
6 a



1 log
3 x
 log
3
5
2 log
3
3 log a
3
 b

4 log
3
4 log
3 b c
5
8. log
2
M
9. log
3
4 x
2
10. log a
5 b
2 c
3
11. 1.3652
12. 0.2789
13. 125
14. 3.1610
15. 800
16. 4
17. 8
18. 8
19. 1.0913
20. 4
21. A = $5500
22. t = 216.096 days
23. t = 14.078 years
24. N = 98.963 kg
25. h = 9 hours
Unit 11 Review