7
Extra Example 7.6
Solve the equation.
a. 18 x 5 10 about 0.797
b. log2 2x 1 log2 (x 1 4) 5 6 4
CHAPTER REVIEW
7.6
Solve Exponential and Logarithmic Equations
pp. 515–522
EXAMPLE
Solve the equation.
Extra Example 7.7
7x 5 12
a.
Write an exponential function y 5
ab x whose graph passes through
(2, 45) and (4, 405). y 5 5 p 3 x
b. log 2 (3x 2 7) 5 5
log7 7 5 log 7 12
2log2 (3x 2 7) 5 25
x 5 log 7 12
3x 2 7 5 32
x
log 12
log 7
x 5 } ø 1.277
EXAMPLES
2, 5, and 6
on pp. 516–518
for Exs. 32–34
7.7
x 5 13
EXERCISES
Solve the equation. Check for extraneous solutions.
32. 5x 5 32 about 2.153
33. log3 (2x 2 5) 5 2 7
34. ln x 1 ln (x 1 2) 5 3
about 3.592
Write and Apply Exponential and Power Functions
pp. 529–536
EXAMPLE
Write an exponential function y 5 ab x whose graph passes through (21, 2) and
(3, 32).
Substitute the coordinates of the two given points into y 5 ab x .
2 5 ab21
32 5 ab
3
Substitute 2 for y and 21 for x.
Substitute 32 for y and 3 for x.
Solve for a in the first equation to obtain a 5 2b, and substitute this expression for
a in the second equation.
32 5 (2b)b3
Substitute 2b for a in second equation.
32 5 2b4
Product of powers property
16 5 b
4
Divide each side by 2.
25b
Because b 5 2, it follows that a 5 2(2) 5 4. So, y 5 4 p 2x .
Chapter Test, p. 543
y
1.
EXERCISES
EXAMPLES
1 and 5
on pp. 529–532
for Exs. 35–38
2
21
Write an exponential function y 5 ab x whose graph passes through the points.
x
35. (3, 8), (5, 2) y 5 64 }1
2
12
37. (2, 9), (4, 324) y 5 }1 p 6 x
4
38. SPORTING GOODS A store begins selling a new type of basketball shoe. The
table shows sales of the shoe over time. Find a power model for the data. y 5 28.0x 0.750
y
542
1
21
x
36. (22, 2), (1, 0.25) y 5 }1 }1
2 2
12
x
2.
Take the positive fourth root because b > 0.
Week, x
1
2
3
4
5
6
Pairs sold, y
28
47
64
79
94
107
Chapter 7 Exponential and Logarithmic Functions
x
3.
4.
f(x)
5.
y
6.
y
g(x)
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laa211se4
1
21
x
1
21
1
x
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1
x
21
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x
7
CHAPTER TEST
Additional Resources
Graph the function. State the domain and range. 1–9. See margin for art.
2. y 5 2 p 4x 2 2 domain: all
1. y 5 3x domain: all real
3. domain: all
real numbers,
range: y < 3
numbers, range: y > 0
4. y 5 4(0.25) x domain: all
real numbers, range: y > 0
1 e2x
7. y 5 }
domain: all real
2
Evaluate the logarithm without using a calculator.
1
11. log 2 }
25
32
Chapter Test, Levels A, B, C
Standardized Chapter Test
• SAT/ACT Chapter Test
• Alternative Assessment
•
1 2 domain: all
real numbers, range: y > 2
all real numbers, range: y > 1
10. log5 25 2
x
1 2
2
6. g(x) 5 }
3
8. y 5 2.5e20.5x 1 1 domain:
numbers, range: y > 0
Assessment Book
3. f(x) 5 25 p 2 x 1 3 1 3
real numbers, range: y > 0
x12
1
5. y 5 2 1 }
domain: all
32
real numbers, range: y > 0
1ex 2 1 2 2
9. h(x) 5 }
3
domain: all real numbers,
range: y > 22
•
Test Generator
Chapter Test
12. log 6 1 0
Easily-readable reduced copies (with answers) of Chapter
Test B, the Standardized
Chapter Test, and the
Alternative Assessment from
the Assessment Book can be
found on pp. 476E–476F.
Graph the function. State the domain and range. 13–15. See margin for art.
13. y 5 log 2 x domain: x > 0,
14. y 5 ln x 2 3 domain: x > 0,
49
16. 2 ln 7 2 3 ln 4 ln }
64
17. log4 3 1 5 log4 2 log4 96
range: all real numbers
Condense the expression.
range: all real numbers
domain: x > 23, range:
all real numbers
18. log 5 1 log x 2 2 log 3
5x
log }
9
Use the change-of-base formula to evaluate the logarithm.
19. log5 50 about 2.431
15. f(x) 5 log (x 1 3) 1 2
20. log 6 23 about 1.750
21. log 9 45 about 1.732
13.
y
Solve the equation. Check for extraneous solutions.
22. 72x 5 30 about 0.874
23. 3 log (x 2 4) 5 6 104
1
24. log4 x 1 log4 (x 1 6) 5 2
21
2
25. Write an exponential function y 5 ab x whose graph passes through (21, 48)
x
and (2, 6). y 5 24 }1
2
26. Write a power function y 5 ax b whose graph passes through (3, 8) and (6, 15). y 5 2.95x 0.907
x
12
14.
27. LANDSCAPING From 1996 to 2001, the number of households that purchased
y
1
x
21
lawn and garden products at home gardening centers increased by about
4.85% per year. In 1996, about 62 million households purchased lawn and
garden products. Write a function giving the number of households H (in
millions) that purchased lawn and garden products t years after 1996. H 5 62(1.0485) t
28. FINANCE You deposit $2500 in an account that pays 3.5% annual interest
15.
compounded continuously. What is the balance after 8 years? $3307.82
29. EARTH SCIENCE Rivers and streams carry small
particles of sediment downstream. The table
shows the diameter x (in millimeters) of several
particles of sediment and the speed y (in meters
per second) of the current needed to carry each
particle downstream.
Type of sediment
x
y
0.2
0.10
Gravel
5
0.50
Mud
Coarse gravel
11
0.75
Pebbles
20
1.00
b. Find a power model for the original data.
Small stones
45
1.50
Estimate the speed of the current needed
to carry a particle with a diameter of
120 millimeters downstream. y 5 0.224x 0.500 ; about 2.45 m/s
Chapter Test
7.
1
a. Draw a scatter plot of the data pairs (ln x, ln y).
See margin.
8.
y
9.
y
f(x)
21
29a.
x
ln y
1
21
ln x
543
h(x)
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1
2
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x
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x
x
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