WorksheetsExponential & Logarithmic Functions Review
Total questions: 55
Worksheet time: 2hrs 35mins
Name
Class
Date
1.
(53x2y4)0
a)
5xy
b)
1
c)
0
d)
5
2.
(y9)-2
a)
y18
b)
y11
c)
1/y18
d)
y9/2
3.
What type of function is
y = 7(5/4)x?
y = 7(5/4)x?
a)
Exponential Growth
b)
Exponential Decay
c)
Linear
d)
None of the above
4.
Which of the following functions shows an initial amount of $15 and an increase of 35% each year?
a)
y = 15(35)x
b)
y = 15(1.35)x
c)
y = 15(0.35)x
d)
y = 35(1.15)x
5.
Rewrite logb(xn)
a)
nlogbx
b)
(logbx)n
c)
xnlogbx
d)
logb(xn)
6.
Evaluate logb(b)
a)
-1
b)
0
c)
1
d)
b
7.
Evaluate blogb(x)
a)
x
b)
b
c)
1
d)
0
8.
Expand log6(5x3/y).
a)
log65x3-log6y
b)
log65+log6x3-log6y
c)
log65+3log6x-log6y
9.
Write the expression as a single logarithm. Then simplify if possible.
log 6 - log 3 + 2 log 7
log 6 - log 3 + 2 log 7
a)
log 98
b)
log 78
c)
log 56
d)
log 45
10.
Write as a single log: log 12 + 2 log x
a)
log (12 + 2x)
b)
log (14x)
c)
log (12 * 2x)
d)
log (12x2)
11.
Solve:
log (4x − 5) = log (2x − 1)
log (4x − 5) = log (2x − 1)
a)
0
b)
1
c)
2
d)
3
12.
log78=
a)
1.069
b)
.936
c)
.903
d)
1.892
13.
7x=17
a)
x=1.456
b)
x=.687
c)
x=1.546
d)
x=.786
14.
log2(x + 5) = 3
a)
3
b)
4
c)
5
d)
6
15.
Evaluate.
log6(1/216)
log6(1/216)
a)
3
b)
1/3
c)
-1/3
d)
-3
16.
Rewrite logvn = a in exponential form.
a)
va = n
b)
na = v
c)
vn = a
d)
an = v
17.
Rewrite 34 = 81 in logarithmic form.
a)
log34 = 81
b)
log813 = 4
c)
log381 = 4
d)
log481 = 3
18.
Solve for x:
logx 25 = 2
logx 25 = 2
a)
5
b)
-5
c)
1/5
d)
-1/5
19.
ln e5=
a)
e5
b)
ln 5
c)
5
d)
5e
20.
What is the domain of the graph?
a)
(-∞,∞)
b)
(-2, ∞)
c)
(0,∞)
d)
(-∞,2)
21.
What is the range of the graph?
a)
(-∞,∞)
b)
(-2, ∞)
c)
(0,∞)
d)
(-∞,2)
22.
What is the range of the graph?
a)
(-∞,∞)
b)
(-2, ∞)
c)
(0,∞)
d)
(-∞,-2)
23.
What is the domain of the graph?
a)
(-∞,∞)
b)
(-2, ∞)
c)
(0,∞)
d)
(-∞,-2)
24.
What kind of asymptotes do logs have?
a)
horizontal ( y=0)
b)
vertical (x=0)
25.
Which has a horizontal asymptote?
a)
exponential
b)
logarithm
c)
both
26.
Which is the change of base formula
a)
log b M = log M / log B
b)
A log with a base of e
c)
A log with a base of e
d)
log M – log N = log M / N
27.
What property is this: log M + log N = log M(N)
a)
private property of logs
b)
power property of logarithms
c)
quotient property of logs
d)
product property of logs
28.
What property is this: log Mx = x(log M)
a)
product property of logs
b)
quotient property of logs
c)
private property of logs
d)
power property of logs
29.
What property is this: log M – log N = log M / N
a)
quotient property of logs
b)
product property of logs
c)
private property
d)
power property of logs
30.
Use change of base to solve:
log 17 132
log 17 132
a)
log 17 / log 132
b)
132 / 17
c)
log 132 / log 17
31.
What relationship is demonstrated by this table of values?
a)
Linear
b)
Exponential
c)
Neither
32.
Evaluate
f(x) = 3x ; f(-4) = ____
f(x) = 3x ; f(-4) = ____
a)
-81
b)
81
c)
1/81
d)
-1/81
33.
The amount of ants in a colony, f, that is decaying can be modeled by f(x) = 800(.87)x, where x is the number of days since the decay started. By what percentage is the colony decaying?
a)
87%
b)
13%
c)
800%
d)
8.7%
34.
The expression 12(1.015)t models the population of elephants in a wildlife refuge after t years since 1975.
Is the population of elephants increasing or decreasing?
Is the population of elephants increasing or decreasing?
a)
Increasing
b)
Decreasing
35.
Write the expression as a single logarithm. Then simplify if possible.
log53 + log56 + log59
log53 + log56 + log59
a)
log569
b)
log556
c)
log5162
d)
log598
36.
Write the expression as a single logarithm. Then simplify if possible.
log 6 - log 3 + 2 log 7
log 6 - log 3 + 2 log 7
a)
log 98
b)
log 78
c)
log 56
d)
log 45
37.
The expression a logx(y5) is equivalent to
a)
5x
b)
5y
c)
5 logxy
d)
5 logyx
38.
Which function is exponential?
a)
f(x)
b)
h(x)
c)
g(x)
39.
What transformations have happened to y = 2x if the new equation is
y = -2(x+3) -6
y = -2(x+3) -6
a)
It stayed the same
b)
flips, up 3, left 6
c)
flips, right 3, down 6
d)
flips, left 3, down 6
40.
are these inverse functions
a)
no
b)
yes
c)
no way to tell
41.
are these inverse functions?
a)
no
b)
yes
c)
no way to tell
42.
log2(x + 5) = 3
a)
3
b)
4
c)
5
d)
6
43.
Solve 8 = 25x+7
a)
x = ⅘
b)
x = ¼
c)
x = -⅘
d)
x = -¼
44.
Solve for x:
42x + 1 = 17
42x + 1 = 17
a)
x = 1
b)
x = -1
c)
x = 2
d)
x = -2
45.
Evaluate the expression.
log77-0.89
log77-0.89
a)
7
b)
7-0.89
c)
-0.89
d)
1
46.
Solve the exponential equation algebraically. (Round to three decimal places)
14e3x+2=560
14e3x+2=560
a)
0.563
b)
3.689
c)
1.442
d)
1.896
47.
Evaluate the expression:
log3 1/243
log3 1/243
a)
1/5
b)
-5
c)
-1/5
d)
5
48.
Evaluate the expression:
log343 7
log343 7
a)
3
b)
-3
c)
49
d)
1/3
49.
Solve:
log5 7x = 2
log5 7x = 2
a)
x = 5/7
b)
x = 25/7
c)
x = 2/7
d)
x = 17.5
50.
Solve for n:
23n = 4
23n = 4
a)
2
b)
3
c)
2/3
d)
4
51.
Solve for x:
2x+6=25
2x+6=25
a)
-1
b)
11
c)
1
d)
-11
52.
Solve: 98-x = 27x-3
a)
5
b)
-5
c)
1/5
d)
-1/5
53.
Solve for b:
363b = 216b+4
363b = 216b+4
a)
6
b)
1
c)
4
d)
-4
54.
Write logb(x/y) as two logs
a)
logbx-logby
b)
logbx+logby
c)
logbx*logby
d)
logbx/logby
55.
Solve the following for 'x';
log6(3x - 2) = log6(5x - 8)
log6(3x - 2) = log6(5x - 8)
a)
x = 3
b)
x = 2
c)
x = -1
d)
No Solution
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