Download Practice B - Spokane Public Schools

Name ________________________________________ Date __________________ Class__________________
Practice B
LESSON
7-5
Exponential and Logarithmic Equations and Inequalities
Solve and check.
2. 122x − 8 = 15
1. 52x = 20
________________________
_________________________
x+7
5x
3. 2x + 6 = 4
0.2x
4. 16 = 64
5. 243
________________________
= 81
x+5
_________________________
x
⎛ 1⎞
7. ⎜ ⎟ = 162
⎝2⎠
⎛ 1 ⎞
8. ⎜ ⎟
⎝ 32 ⎠
________________________
2x
= 64
_________________________
________________________
6. 25x = 125x – 2
________________________
⎛ 1 ⎞
9. ⎜
⎟
⎝ 27 ⎠
x −6
= 27
________________________
Solve.
10. log4 x5 = 20
11. log3 x6 = 12
________________________
13. log x − log 10 = 14
_________________________
14. log x + log 5 = 2
________________________
16. log (x + 4) − log 6 = 1
_________________________
2
17. log x + log 25 = 2
________________________
_________________________
12. log4 (x − 6)3 = 6
________________________
15. log (x + 9) = log (2x − 7)
________________________
18. log (x − 1)2 = log (−5x − 1)
________________________
Use a table and graph to solve.
19. 2 x − 5 < 64
________________________
20. log x3 = 12
_________________________
21. 2x 3x = 1296
________________________
Solve.
22. The population of a small farming community is declining at a rate of 7%
per year. The decline can be expressed by the exponential equation
P = C (1 − 0.07) t , where P is the population after t years and C is the current
population. If the population was 8,500 in 2004, when will the population be
less than 6,000?
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7-36
Holt Algebra 2
SECTION 7A
Quiz for Lesson 7-1 Through 7-4
7-1 Exponential Functions, Growth, and Decay
Tell whether the function shows growth or decay. Then graph.
1
1. f (x) = _
4
x
1 (0.2)
2. f (x) = _
5
()
x
3
4. f (x) = 6.4 1_
8
( )
3. f (x) = 14(1.4 x)
x
5. Suppose that the number of bacteria in a culture was 1000 on Monday and the
number has been increasing at a rate of 50% per day since then.
a. Write a function representing the growth of the culture per day.
b. Graph the function, and use the graph to predict the number of bacteria in the culture
the following Monday.
7-2 Inverses of Relations and Functions
Graph each relation. Then graph its inverse.
6.
x
-1
0
1
2
3
y
0
4
8
12
16
7.
x
0
1
2
3
4
y
-1
1
-_
3
1
_
3
1
2
1_
3
Graph each function. Then write and graph the inverse.
3 -x
9. f (x) = _
4
8. f (x) = x + 2.1
10. f (x) = 5x + 4
x + 1.5
11. f (x) = 0.4 _
2
(
)
12. Rebekah’s computer repair bill includes $210 for parts and $55 per hour for labor.
Her bill can be expressed as a function of hours x by f (x) = 210 + 55x. Find the
inverse function. Use it to find the number of hours of labor if her bill was $402.50.
7-3 Logarithmic Functions
Write the exponential equation in logarithmic form.
13. 3 2 = 9
14. 17.6 0 = 1
15. 2 -2 = 0.25
16. 0.5 x = 0.0625
Write the logarithmic equation in exponential form.
17. log 4 64 = 3
18. log _1 25 = -2
19. log 0.99 1 = 0
5
20. log e x = 5
x
5 ; x = -1, 0, 1, 2, 3. Then graph the inverse function.
21. Use the given x-values to graph f (x) = _
6
()
7-4 Properties of Logarithms
Express as a single logarithm. Simplify, if possible.
22. log 3 81 + log 3 9
23. log _1 25 + log _1 5
24. log 1.2 2.16 - log 1.2 1.5
26. log 7 343
27. 17 log 17 0.73
29. log 10 0.01
30. log 5 625
5
5
Simplify each expression.
25. log 4 256 2
Evaluate.
28. log 27 243
Ready to Go On?
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