Mathematics Department
Logarithmic Functions
MAT 140 - College Algebra - Gateway 4: Exponential and
Name:
Date:
19191–A
• This exam covers material from Sections 6.1 - 6.4.
• Students MAY NOT use a graphing calculator on this exam.
• Unless otherwise indicated exact answers, i.e.
decimal approximations.
1
3
or
p
7, should be given rather than
• A 70% or higher AVERAGE on all gateway exams is required to pass College Algebra
with a C or better. You may retake the exam at most once per day.
• The highest grade on the exam is what will be recorded.
• Note that by earning an 80% or more ON EACH of the first 4 gateway exams, you will
be exempt from the last gateway exam.
Exponential and Logarithmic Expressions
1.
Evaluate log7
1
.
49
(1)
2.
Approximate log6 10 to three decimal places.
(2)
Exponential and Logarithmic Equations
3.
Solve the equation ln (3x + 7) = 4.
(3)
4.
Find an exponential equation that is equivalent to log2 (x 7) =
(4)
5.
Solve the equation e5x+4 = 14.
(5)
6.
Solve the equation ex+4 =
1
.
e3
(6)
7.
8.
Solve the equation 33 · 32x
Solve the equation 3(55x+2
5
= 729.
(7)
5) = 360.
(8)
9.
Find a logarithmic equation that is equivalent to 77x
3
= 7.
(9)
Exponential and Logarithmic Functions
10. Given g(x) = log6 (x + 7), solve the equation g(x) = 5.
(10)
6.
1
11. Given g(x) = log6 ( x+2
), what is the numerical value of g(1294)?
(11)
12. If f (x) = 4x + 4 and g(x) = x2 + 6x + 4, determine g(f ( 2)).
(12)
p
13. Given f (x) =
5x 20, which of the following is NOT in the domain of f ?
(A)
10
(B)
11
(C)
13
(D)
9
(E) All of the above are in the domain of f
Applications
14. If $1569 is invested in a bank acccount where interest is compounded semiannually
at a rate of 3%, the amount of money in the bank in t years is approximated by
A(t) = 1569e0.03t . What is the amount of money in the bank (rounded to the nearest
cent) after 4 years?
(14)
15. If $3272 is invested in a bank acccount where interest is compounded continuously
at a rate of 1.5%, the amount of money in the bank in t years is approximated by
A(t) = 3272e0.015t . How many years (rounded to the nearest tenth of a year) will it
take the investment to be worth $4418?
(15)
Mathematics Department
Logarithmic Functions
Name:
MAT 140 - College Algebra - Gateway 4: Exponential and
ANSWER KEY
Exponential and Logarithmic Expres-
Date:
Applications
sions
14. $1769.04
1.
2
15. 20.0 years
2. x = 1.285
Exponential and Logarithmic Equations
3. x =
e4
7
3
6
4. x
7=2
5. x =
ln (14)
5
6. x =
4
7
7. x = 4
8. x =
1
5
9. 7x
3 = log7 (7)
Exponential and Logarithmic Functions
10. x = 7769
11.
4
12.
4
13. E
19191–A