TEST REVIEW 2MP
Part 1 (No Calculator)
1
1. log 4
=
16
4. log b 125 = 3 , find b
2. log 7 1 =
5. log 36 x = −
3. log 9 3 =
1
2
6. log 1 x = −2
5
7. Rewrite using exponents:
a. log 4 r = m
8. Rewrite using logs:
a. d k = 14
b. log k = 5
b. 6 2c = 18
10. Expand:
! 2xy $
log # 5 & =
" 3z %
11. Express as a single logarithm:
1
1
log b r + log b s − log b w =
2
2
13. Solve for x : (Check your solutions)
log 6 x + log 6 (x −1) = 1
14. Describe each of the following functions as growth or decay and state
the rate of increase or decrease.
9. y = 12 ⋅ 8 x if y = 48 , find x
12. Simplify and evaluate:
(Use properties of logarithms.)
log 9 25 − log 9 75 =
a. f (x) = 10(.9)x
b. f (x) = 6(5)x
c. f (x) = 1.23x
15. The graph of f (x) = 12 ⋅ 4 3x −1 is
identical to the graph of:
a. 3 ⋅ 4 3x
c. 3 ⋅ 64 x
1
⋅ 64 x
3
d. 4 ⋅ 4 x
b.
16. Solve for x :
log 7 3x = log 7 16 − log 7 8 + log 7 9
17. Solve for x :
9 2−x = 27 x+2
18. The function graphed to the right could be the
graph of:
a.
b.
c.
d.
-2
2
-2
f (x) = −3 ⋅ 3x
f (x) = −1⋅ 3x − 3
f (x) = −3 ⋅ 3x −1
f (x) = −1⋅ 9 x
-4
-6
-8
Part 2 (With Calculator)
19. Solve for x , using logs:
26 x = 19
21. Find Domain and range of f (x) = 2 ⋅ 3x
20. Solve for x , using logs:
2 ⋅15 x = 90
22. How many years would it take for the population
growing at a rate of 1.1% per year to triple in size?
23. Let f (x) = log 3 (x) Write a formula for the following transformations of f (x)
a. f (x) down 10 units.
b. f (x) right 4 units
c. f (x) Reflected over x axis
d. f (x) Horizontally stretched by 5
e. f (x) Vertically stretched by 2
24. The number of bacteria in a petri dish double every 25. The exponential growth model A = 208e 0.008t gives
3 hours. Initially, there are 2500 bacteria present. the population of the United States, in millions, after
When will there be 100,000 bacteria?
1970. In what year will the population of the United
States be 300 million?
26. An initial deposit of $2800 is made in a savings account for which the interest is compounded continuously.
The balance will triple in 8 years. What is the annual rate of interest for this account?
27. A radioactive substance undergoes exponential decay. If 40% of the original amount decays in 5 years, by
what percent does the substance decay each year?
Answer Key for problems 1-27: (there are 3 mistakes here!!!!)
1. -2
2. 0
6. 25
7. 4 m = r
3.
8. log d 14 = k
10 5 = k
11. log b
rs
w
12. -
1
2
4. 5
1
2
9.
log 6 18 = 2c
13. x=3
2
3
14.
5.
1
6
10.
log 2 + log x + log y − log 3 − 5 log z
15.
a. or
b.
decay 10%,
growth 500%,
growth 23%
16. x=6
17.
18. c.
2
5
19. x=0.9037
21. Domain: all real numbers. Range: y ≥ 0
23. log 3 (x) − 10
25. t=45.753
or 2015 year
log 3 (x − 4)
26.
− log 3 (x)
13.73%
20. x=1.405
22. 100.422 years
!1 $
log 3 # x &
"5 %
27.
2 log 3 (x)
9.72 % decay
24. 15.965 hours
Extra Credit problems. (0.5 point each) Show all work. Circle your final answers.
1. Given that 3x+2 y = 27 and 2 2 x+y = 8 , find x − y
2. Combine as one logarithm:
x
log xy + 2 log x − log y − log =
y
3.
4.
Solve for x :
2 x − 2 x−1 = 32
If log a b = 5 then log b a = ?
5. Suzy’s uncle put $1,000 in the bank for her
when she was born. How much will be in the
account on her 16th birthday, if the bank pays 8%
compounded quarterly?
6. The population of Suzyville has been growing at an
annual rate of 12.5% since Suzy became mayor in 2003. If
the population was 1802 in 2008, what was the population
in 2003?
7. The half life of an element is 347 days. If Suzy
started out with 1200 grams of the element, how
long will it be before only 238 grams remain?
8. Suzy took some ibuprofen. The amount of ibuprofen in a
person’s bloodstream decreases by 29% each hour. If she
took 300 mg when she got up at 7:00 am, how much is still
in her bloodstream when she goes to bed at 10:00 pm?
9. Suzy was doing an experiment with bacteria. She
has a petri dish with 2,300 bacteria in it. At what
rate are they growing per hour, if after 9 hours
there are 53,991?
10. Suzy was another experiment on fruit fly reproduction.
After 3 days, she had 250 flies. After 7 days, she had 900
flies. Write an exponential model in the form y = ab x .