Math 230 Practice Test 4
NOTE: This review is designed to help you prepare for the test. It does not necessarily
cover all of the material for which you are responsible. For a complete review, study
your notes, in-class assignments, and homework.
For 1 – 3 use:
13 xxf
and
5
2
xxg
1.
2fg
2.
xgf
3.
xf
1
4. Show that
73 xxf
and
3
7
3
1
1
xxf
are inverses using composition.
5. Graph:
23
x
y
6. Graph:
xy
5
log
7. a) Solve:
3125log
x
b) Solve:
3ln x
8. Expand in terms of the individual logarithms x, y, and z with coefficient 1.
zy
x
b3
2
log
9. Condense as a single logarithm and simplify:
xyx
aaa
log2log5log
2
1
10. Given
23.15log
b
and
15.03log
b
find
3
5
log
b
.
11. Approximate to 3 decimal places:
7log
5
12. Solve and approximate to 3 decimal places:
75
x
13. Solve:
1log9log
1010
xx
14. Graph:
32
2
yyx
15. Graph:
3649
22
yx
16. Graph:
01095016254
22
yxyx
17. Find the equation of the circle with center
2,3
and passing through
2,11
.
18. In 1967, Dr. Chrisiaan Barnard of South Africa stunned the world by performing
the first heart transplant. There were 1418 heart transplants in 1987, and 2185 such
transplants in 1999. Use the equation
kt
ePP
0
to find an equation that fits the data
from 1987 and 1999. Use the function to predict the number of heart transplants in 2012.