Math 230 Intermediate Algebra
Practice for EXAM #3
1. For the functions
32 xxf
and
45
2
xxxg
find:
a.
xgf
b.
1fg
c.
33 gf
d.
xgf
e.
xf
1
2. a. Graph
3
2)(
x
xg
b. Graph
xxf
2
log3)(
3. Are the functions in problems 1 and 2 inverses of each other?
Explain or justify your answer.
4. a. Express as a single logarithm with coefficient 1:
zyx
999
log3log2log3
b. Write the logarithm in expanded form:
zy
x
2
4
log
5. Evaluate the following: a.
25
1
5
log
b.
9log
2
6. Solve for x: a.
342
8127
xx
b.
75
2
x
c.
1
3
27
log
5
x
x
Solve:
7.
10)32ln(3 x
8.
4loglog)2(log
888
xx
9.
2log)32log(log xx
10. An investment is made into a trust fund at an annual interest rate of
4
3
7
%,
compounded quarterly. How long will it take for the investment to double?
11. Francium-223 is a very rare radioactive isotope discovered in 1939 by Marguerite
Percy. In a laboratory, a 3-microgram sample of francium-223 will decay to 2.54
micrograms in 5 min. What is the half-life of francium-223, in minutes?