WorksheetsLogarithmic Functions
Total questions: 64
Worksheet time: 2hrs 34mins
Name
Class
Date
1.
Given y=3x determine the y-intercept
a)
(0,1)
b)
(0,3)
2.
Compare f(x) = 3x- 4 with the basic function g(x) = 3x
a)
4 units up
b)
4 units to the left
c)
4 units to the right
d)
4 units down
3.
What equation matches the graph?
a)
f(x) = 3x
b)
f(x) = (⅓)x
c)
f(x) = log₃(x)
4.
Write in logarithmic form.
52 = 25
52 = 25
a)
log52 = 25
b)
log225 = 5
c)
log255 = 2
d)
log525 = 2
5.
Is the pictured graph growth, decay, or linear or none?
a)
Exponential Growth
b)
Exponential Decay
c)
Linear
d)
None
6.
The common logarithm has what base?
a)
10
b)
0
c)
e
d)
-e
7.
Classify the given graph.
a)
exponential growth
b)
exponential decay
c)
positive linear
d)
negative linear
8.
Find the domain and range of:
f(x) = log2(x)
f(x) = log2(x)
a)
D: all real numbers
R: y > 0
R: y > 0
b)
Domain: all real numbers
Range: all real numbers
Range: all real numbers
c)
Domain: x > 0
Range: all real numbers
Range: all real numbers
d)
Domain: all real numbers
Range: y < 0
Range: y < 0
9.
What is the asymptote of y = log2x ?
a)
y = 0
b)
x = 0
10.
What is the asymptote of y = log2x ?
a)
y = 0
b)
x = 0
11.
What is the asymptote of y = log2x - 3
a)
y = 0
b)
y = -3
c)
x = 0
d)
x = -3
12.
What is the asymptote of y = log2(x - 3) ?
a)
y = 0
b)
y = 3
c)
x = 0
d)
x = 3
13.
The asymptote of y = log2x + 1 will shift...
a)
right one to x = 1
b)
left one to x = -1
c)
not shift at all and remain x = 0
14.
The asymptote of y = log2(x + 2) will shift...
a)
right two to x = 2
b)
left two to x = -2
c)
not shift and remain x = 0
15.
Classify the following graph.
a)
Exponential Growth
b)
Exponential Decay
c)
Logarithmic
16.
Which has a vertical asymptote?
a)
Exponential
b)
Logarithmic
c)
Both
17.
Which has a horizontal asymptote?
a)
Exponential
b)
Logarithmic
c)
Both
18.
What is the domain?
a)
(-∞, ∞)
b)
(0, ∞)
c)
[1, ∞)
d)
(1, ∞)
19.
What is the equation of the asymptote?
a)
x = -3
b)
x=5
c)
y= -3
d)
y=5
20.
What are the transformations of this graph?
a)
Right 1 Up 5
b)
Right 1 Down 5
c)
Left 1 Up 5
d)
Left 1 Down 5
21.
What is the Range?
a)
y > 0
b)
All Real Numbers
c)
y > 1
d)
y < 1
22.
What is the Domain?
a)
x > 0
b)
All Real Numbers
c)
x > 1
d)
x < 1
23.
Logarithmic functions are the inverse of...
a)
Linear Functions
b)
Exponential Functions
c)
Quadratic Functions
d)
Polynomial Functions
24.
What is the parent function seen here?
a)
Logarithmic
b)
Exponential
c)
Square Root
d)
Constant Function
25.
List the domain for the following.
a)
(-2, ∞)
b)
(-∞, ∞)
c)
(- ∞,4)
d)
(1/5, ∞)
26.
Describe the transformations of f(x)= -log2(x+1)
a)
left one & y-axis reflection
b)
right one & y-axis reflection
c)
left one & x-axis reflection
d)
right one & x-axis reflection
27.
Match the graph with its equation
a)
y = log6(-x) + 1
b)
y = log6(x − 2) + 1
c)
y = log6(x + 2) - 1
d)
y = log(x-8) + 1
28.
Match the graph with its equation
a)
y = log5 (x + 1) + 1
b)
y = log5 (x - 1) + 1
c)
y = log5 (x2) + 1
d)
y = log5 (x)-1
29.
Match the graph with its equation
a)
y = log4 (x)+2
b)
y = log4 (x + 2) + 1
c)
y = log4 (x - 1) + 2
d)
y = log4 (-x + 2)
30.
Write each equation in its equivalent exponential form.
6=log264
6=log264
a)
264=64
b)
64=2x
c)
y=x64
d)
26=64
31.
Write each equation in its equivalent exponential form.
4=log216
4=log216
a)
23=16
b)
2x=16
c)
2y=16
d)
24=16
32.
Write each equation in its equivalent exponential form.
2=log3x
2=log3x
a)
3x=2
b)
2x=3
c)
32=x
d)
x3=2
33.
Write each equation in its equivalent logarithmic form.
∛8=2
∛8=2
a)
log1/38=2
b)
log28=⅓
c)
log38=2
d)
log82=1/3
34.
Write each equation in its equivalent logarithmic form.
∛64 = 4
∛64 = 4
a)
log464=⅓
b)
log644=3
c)
log644=⅓
d)
logxy=1
35.
The graph of a logarithmic function is given. Select the function for this graph
a)
f(x) = 1 - log3 x.
b)
f(x) = 1+ log3x
c)
f(x) = log10 (3x +1)
d)
f(x) =-log3x
36.
Evaluate this expression:
log21/8 =
log21/8 =
a)
-5
b)
1/6
c)
-3
d)
3
37.
Evaluate log41
a)
1
b)
0
c)
4
d)
undefined
38.
A logarithm to the base e.
a)
Common Log
b)
Natural Logarithm
c)
Logistic Model
d)
Gaussian Model
39.
Write the equation for the graph.
a)
f(x) = log2 (x-3)
b)
f(x)= 3 log2(x)
c)
f(x) = log2(x+3)
d)
f(x) = log2(x) + 3
40.
What is the range of the graph?
a)
(-∞,∞)
b)
(-2, ∞)
c)
(0,∞)
d)
(-∞,2)
41.
The inverse of a logarithmic function and the logarithmic function do what on a graph?
a)
The are perpendicular
b)
They are paralell
c)
They reflect over the line y=x.
d)
There is nothing special .
42.
What kind of asymptotes do logs have?
a)
horizontal ( y=0)
b)
vertical (x=0)
43.
Rewrite logpt = m in exponential form.
a)
pt = m
b)
tm = p
c)
mt = p
d)
pm = t
44.
Write logb(xy) as two logs
a)
logbx+logby
b)
logbx-logby
c)
logbx*logby
d)
logbx/logby
45.
Write logb(x/y) as two logs
a)
logbx-logby
b)
logbx+logby
c)
logbx*logby
d)
logbx/logby
46.
Evaluate logb(b)
a)
-1
b)
0
c)
1
d)
b
47.
Log with a base "e" (loge) is the same thing as...
a)
"e"
b)
Natural Logarithm (LN)
c)
Common Logarithm (Log)
d)
Natural Log, base "e"
LNe
LNe
48.
Simplify eln(x)
a)
0
b)
1
c)
x
d)
8
49.
Simplify log443x
a)
3x
b)
3
c)
4
d)
43x
50.
Rewrite 34 = 81 in logarithmic form.
a)
log34 = 81
b)
log813 = 4
c)
log381 = 4
d)
log481 = 3
51.
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
52.
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
53.
a)
A
b)
B
c)
C
d)
D
54.
Condense
a)
A
b)
B
c)
C
d)
D
55.
log2(x + 2) + log2x = 3
a)
-4, 2
b)
-2, 4
c)
2
d)
1
56.
4(x-2)= 64(x+1)
a)
-2/5
b)
-5/2
c)
7/2
d)
2/7
57.
Condense: log26+log23=
a)
log218
b)
log22 = 1
c)
log23
d)
log29
58.
Condense
a)
logxyz3
b)
log(xy/z3)
c)
logx+logy+logz3
d)
logx3y3z3
59.
Expand
a)
log8x+log8y+log8z
b)
5log8x+5log8y+5log8z
c)
log8xy+5log8z
d)
log8x+log8y+5log8z
60.
log(10 - 4a) = log(-3a + 8)
a)
-1
b)
2
c)
No Solution
d)
-13/3
61.
log(- 4x - 6) - log(6) = log(64)
a)
-195/2
b)
-14/3
c)
-2
d)
No Solution
62.
Expand log3(9x2)
a)
3+2log3x
b)
log39+2log3x
c)
2+2log3x
d)
log9+2logx
63.
6x+2 = 18
a)
0.3869
b)
-0.3869
c)
1.3869
d)
-1.7594
64.
a)
log (a5 + b25)
b)
log (a5 − b25)
c)
log (ab25)
d)
log (a5/b25)
100 %
