Name: ________________________ Class: ___________________ Date: __________ ID: A
Honors Math 3 Unit 2 TEST, Exponential and Logarithmic Functions
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Expand the logarithm completely. Do not change the base. log 6 x 5 y 2
a. 5log 6 x + 2 log 6 y c. 5log 6 x ⋅ 2log 6 y
(m + n)
b. log 6 (x 5 ) + log 6 (y 2 ) d. log b (xy)
xy
____ 2. Expand the logarithm completely. Do not change the base. log 8
6
log 8 x ⋅ log 8 y log 8 x ⋅ log 8 y
a. c.
6 log 8 6
log 8 x + log 8 y
b. d. log 8 x + log 8 y − log 8 6
6
____ 3. Write the logarithmic expression as a single logarithm: 4logx + logy
a. log(xy) 4 b. log(4x + y) c. 4logxy d. log x 4 y
____ 4. Write the logarithmic expression as a single logarithm: log 3 7 + log 3 x − 9log 3 y
7x x+7
a. log 3 (7x − y 9 ) b. log 3 9 c. log3 (7 + x − 9y) d. log 3
y 9y
____ 5. Write the logarithmic expression as a single logarithm: 2log 3 x + log3 6
2
a. 2log 3 6x b. log 3 6x c. log 3 (2x + 6) d. log 3 2x 6
____ 6. Solve for x. lnx − ln5 = 5
a. e 10 b. 500,000 c. e5 + 5 d. x = 5 ⋅ e5
Short Answer
7. Write in logarithmic form: 3 2 = 9 (Don’t simplify) ___________=____________
8. Write in exponential form: log 4 2 = 1 / 2 (Don’t simplify) ___________=____________
9. Evaluate: log 3 243 ___________________
10. Solve: 63x = 235. Round to four decimal places. ___________________
11. Solve: log(6x + 5) = 3 . Round to four decimal places. ___________________
12. Find x:log(x + 58) − log x = 3 Round to four decimal places. ___________________
1
Name: ________________________ ID: A
13. Solve for x. ln2 + lnx = 4 . Round to four decimal places. ___________________
14. Find x: 3e 5x − 6 = 8. Round to four decimal places. ___________________
15. Find x. e x = 13. Round to four decimal places. ___________________
16. Describe the translation from the parent graph using ‘up’, ‘down’, left’, ‘right’ and how many units.
y = x−5 +4 _______________________
17. Describe the translation from the parent graph using ‘up’, ‘down’, left’, ‘right’ and how many units.
y = 2x + 5 + 6 _______________________
18. Describe the translation from the parent graph using ‘up’, ‘down’, left’, ‘right’ and how many units.
y = log(x − 2) − 4 _______________________
19. Write an equation from y = log x with a shift of up 3. _______________________
20. Write an equation from y = log x with a shift of up 4 and left 5.
_______________________
21. You invest $6100 at 3.6% compounded continuously. How much will you have in the account after 8
years? Record your answer to the nearest penny.
Write your initial formula here: _____________________ Write the amt here: $__________
2
Name: ________________________ ID: A
22. Constructed Response: Please read each question carefully and respond to all parts of the question.
Be sure to neatly show all your work in order to receive full credit. Lastly, make sure to justify
answers when instructed to.
Suppose you invest $598 at 50% compounded continuously.
a) Choose an exponential function to model the amount in your investment account.
(1.50t) .50 12t
Circle one: y = 598 ⋅ e .50t y = 598(1.50) t y = 598e y = 598(1 + )
12
b) In how many years will the total reach $3800? Show your work and round
your answers to the nearest tenth. __________
c) You want to know whether you can accrue more interest with an account
that is compounded monthly. Use it to find the number of years it would take the__________
account to reach $3800 if compounded monthly. Round to the nearest tenth.
Essay
23. Graph using a table of values. Use a different color for each graph.
x f(x) f(x) = 5 x
Domain:
-2
-1 Range:
0 f −1 (x) = log 5 x
1 Domain:
2 Range:
3
Name: ________________________ ID: A
24. Graph the piecewise function.
ÏÔÔ ¸Ô
ÔÔ −2x − 8
ÔÔÔ ; −6 ≤ x ≤ −3 ÔÔÔÔ
ÔÔ
y = ÔÌÔ − |x | + 1 ; −3 < x ≤ 1 Ô˝Ô
ÔÔ ÔÔ
ÔÔ ÔÔ
ÔÔÓ log 2 x ; x>1 ÔÔ
˛
Find: (Round to the nearest 100th)
f(2) - 3f(-4) + f(7) = ___________
4
ID: A
Honors Math 3 Unit 2 TEST, Exponential and Logarithmic Functions
Answer Section
MULTIPLE CHOICE
1. ANS: A PTS: 1
2. ANS: D PTS: 1
3. ANS: D PTS: 1
4. ANS: B PTS: 1
5. ANS: B PTS: 1
6. ANS: D
Correct numerical answer: 742.0658
PTS: 1
SHORT ANSWER
7. ANS:
log3 9 = 2
32 = 9
PTS: 1
8. ANS:
2 = 41 / 2
41 / 2 = 2
PTS: 1
9. ANS:
5
5 = log 3 243
PTS: 1
10. ANS:
1.0157
63x = 235
x = 1.0157
PTS: 1
11. ANS:
165.8333
PTS: 1
1
ID: A
12. ANS:
0.0581
A = 58
B=3
PTS: 1
13. ANS:
27.2991
1
Correct numerical answer: ⋅ e 4 = 27.2991
2
PTS: 1
14. ANS:
0.3081
1 8+6
x = (ln( )) =0.3081
5 3
PTS: 1
15. ANS:
2.5649
x = ln(13) = 2.5649
PTS: 1
16. ANS:
PTS: 1
2
ID: A
17. ANS:
PTS: 1
18. ANS:
PTS: 1
3
ID: A
19. ANS:
y = log(x) + 3
PTS: 1
20. ANS:
y = log(x + 5) + 4
PTS: 1
4
ID: A
21. ANS:
a) y = 6100 ⋅ e .0360t
b) $8, 135.92 = 6100e .0360t ; t = 8
PTS: 1
22. ANS:
a) y = 598 ⋅ e .50t
b) 3800 = 598e .50t ; t = 3.7
.50 12t
c) 3800 = 598(1 + ) ; t =3.8
12
PTS: 1
ESSAY
23. ANS:
** f(x) = 5 x ** f −1 (x) = log 5 x
x f(x) f(x) = 5 x
-2 0.0400 Domain: (-inf,
inf)
-1 0.2000 Range: (0,inf)
0 1 f −1 (x) = log 5 x
1 5 Domain: (0,inf)
2 25 Range: (-inf,
inf)
3 125
PTS: 1
5
ID: A
24. ANS:
N=4
ÏÔÔ ¸Ô ÏÔÔ ¸Ô
ÔÔ −2x − 7
ÔÔÔ ; −6 ≤ x ≤ −3 ÔÔÔÔ ÔÔ 2x + 7
ÔÔÔ ; −6 ≤ x ≤ −3 ÔÔÔÔ
ÔÔ ÔÔ
N=1, y = ÔÔÌ −2 |x | + 5 ; −3 < x ≤ 2 ÔÔ˝ N=2, y = ÔÔÌ |x | − 2 ; −3 < x ≤ 4 ÔÔ˝
ÔÔ ÔÔ ÔÔ ÔÔ
ÔÔ ÔÔ ÔÔ Ô
ÔÔ log 2 x ; x>2 ÔÔ ÔÔ log 2 x ; x > 4 ÔÔÔ
Ó ˛ Ó ˛
ÏÔÔ ¸Ô ÏÔÔ ¸Ô
ÔÔ −2x − 8
ÔÔÔ ; −6 ≤ x ≤ −3 ÔÔÔÔ ÔÔ −2x − 8
ÔÔÔ ; −6 ≤ x ≤ −3 ÔÔÔÔ
ÔÔ ÔÔ
N=3, y = ÔÌÔ − |x | + 1 ; −3 < x ≤ 1 Ô˝Ô N=4, y = ÔÌÔ − |x | + 1 ; −3 < x ≤ 1 Ô˝Ô
ÔÔ ÔÔ ÔÔ ÔÔ
ÔÔ ÔÔ ÔÔ ÔÔ
ÔÔÓ log 2 x ; x>1 ÔÔ
˛ ÔÔÓ log 2 x ; x>1 ÔÔ
˛
PTS: 1
