Unit 34 Test Study Guide
(Exponential &
Logarithmic Functions)
Name: __________________________________________
Date: ____________________________ Per: __________
Topic 1: Graphing Exponential & Logarithmic Functions
Directions: Graph each function, then identify its key characteristics.
1. f ( x)
1
3
x 1
4
Domain:
Range:
y-intercept:
Asymptote:
Increasing Interval:
Decreasing Interval:
End Behavior:
2. f ( x)
2 2( x
e
3
1)
5
Domain:
Range:
y-intercept:
Asymptote:
Increasing Interval:
Decreasing Interval:
End Behavior:
3. f ( x)
3 2
( x 2)
6
Domain:
Range:
y-intercept:
Asymptote:
Increasing Interval:
Decreasing Interval:
End Behavior:
© Gina Wilson (All Things Algebra®, LLC), 2017
Topic 2: Exponential vs. Logarithmic Form
Directions: Graph each function, then identify its key characteristics.
4. f ( x)
log3 ( x 4) 2
Domain:
Range:
x-intercept:
Asymptote:
Increasing Interval:
Decreasing Interval:
End Behavior:
5. f ( x)
log 1 3( x 1)
1
Domain:
2
Range:
x-intercept:
Asymptote:
Increasing Interval:
Decreasing Interval:
End Behavior:
6. f ( x)
7
ln( x) 3
4
Domain:
Range:
x-intercept:
Asymptote:
Increasing Interval:
Decreasing Interval:
End Behavior:
© Gina Wilson (All Things Algebra®, LLC), 2017
Topic 3: Evaluating Logarithms
Directions: Rewrite each equation in exponential form.
8. log 1 32
5
7. log3 81 4
9. ln 8
2.08
2
Directions: Rewrite each equation in logarithmic form.
7
11. e4 54.6
10. 4 2 128
12. 104
10, 000
Directions: Evaluate the following. Use the change of base formula when necessary.
14. log 1 625
13. log4 1
5
15. log12 6
16. log8 61
Topic 4: Properties of Logarithms, Condensing & Expanding Logarithms
Directions: Condense each expression into a single logarithm.
1
17. 4 log3 x 2 log3 y
18. (log7 64
3
19.
1
ln 64
2
5 ln k
4 ln m
20. 2 log( x
2 log7 27)
4) log(3 x)
Directions: Expand each logarithm completely.
21. log2 3 4 x
5
22. log4
3a7 c
5
© Gina Wilson (All Things Algebra®, LLC), 2017
5 u
23. log
w2
24. ln(3 x2
3
2 x 8)
Topic 5: Solving Logarithmic Equations
Directions: Solve each equation, rounding to the nearest the-thousandths place when necessary.
Check for extraneous solutions.
26. log9 12 log9 (k 5) log9 (k 6)
25. log(3 x2 4 x) log(2 x2 12)
27.
1
log5 (5c 9)
2
29. ln(2 r
3)
log5 3 log5 2
1
ln 9
2
7
28. log8 (7
5 w)
30. 3 log6 (2h2
11
3
2
14h) 9 15
Topic 6: Solving Exponential Equations
Directions: Solve each equation, rounding to the nearest the-thousandths place when necessary.
Check for extraneous solutions.
31.
1
2
2
43 d
1
32. 243
1
9
u
27
5u
© Gina Wilson (All Things Algebra®, LLC), 2017
33. 183 n
4
35. 5 7 92 r
49
7
34.
20
6 ex
36. 52 x
1
2
5
3x
7
144
Topic 7: Applications (Exponential Growth & Decay, Logistic Growth, Compound Interest)
37. Kevin started his new job with a salary of $26,550. Every year, he receives a 3.15% increase in his
salary. Write and use a continuous exponential growth function to find his salary after 20 years.
38. A 2018 Chevy Tahoe was purchased for $62,625. After 5 years, the vehicle has a value of $35,000.
Write and use a continuous exponential decay function to find the rate of depreciation.
39. A contagious disease started to spread around an apartment complex. After t days, the number
of people who have been infected by the disease is modeled by the function below. Using the
function, determine how many days it will take for 150 people to become infected.
f (t )
350
1 4e 0.07t
© Gina Wilson (All Things Algebra®, LLC), 2017
40. Sharon invests $2,300 into an account that earns 4.25% interest compounded weekly. Assuming
there are no other deposits or withdrawals, find the balance in the account after 18 years.
Topic 8: Nonlinear Regression
41. On January 1, 2013, a deposit of $600 was made into a new investment account. The table
below shows the balance of the account on the first of each successive year, and no other
deposits or withdrawals were made. Use exponential regression to model the data, then
determine what year the account will earn $4,000.
Year
Balance
2013
$600.00
2014
$675.11
2015
$771.64
2016
$865.79
2017
$980.26
42. The table below shows the gym membership sales in each of its first six weeks. Use logarithmic
regression to write an equation to model the data, then find the number of gym memberships
sold in the 20 weeks.
Weeks
Members
1
162
2
187
3
199
4
211
5
220
43. A population of fish is deposited into a local lake. Determine whether an exponential or power
model best fits the data, then use the equation to approximate the number of fish after one-half
of a year.
Weeks
Population
1
78
2
92
3
100
4
106
5
113
6
118
© Gina Wilson (All Things Algebra®, LLC), 2017