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Properties of logarithm May 1 of 2019

Total questions: 45

Worksheet time: 3hrs 16mins

Name
Class
Date
1.
Write logb(xy) as two logs
a)
logbx+logby
b)
logbx-logby
c)
logbx*logby
d)
logbx/logby
2.
Write logb(x/y) as two logs
a)
logbx-logby
b)
logbx+logby
c)
logbx*logby
d)
logbx/logby
3.
Rewrite logb(xn)
a)
nlogbx
b)
(logbx)n
c)
xnlogbx
d)
logb(xn)
4.

Write the expression as a single logarithm. Then simplify if possible.

log52 + log53 + log54

a)

log5 9

b)

log5 234

c)

log5 24

d)

log5 34

5.
Write the expression as a single logarithm.   Then simplify if possible.
log 6 - log 3 + 2 log 7
a)
log 98
b)
log 78
c)
log 56
d)
log 45
6.
Condense
a)
A
b)
B
c)
C
d)
D
7.
a)
6log8(xyz)
b)
log8(x) - log8(y) - 6log8(z)
c)
log8(x) + log8(y) - log8(z)
d)
log8(x) + log8(y) + 6log8(z)
8.
a)
log (a+ b25)
b)
log (a− b25)
c)
log (ab25)
d)
log (a5/b25)
9.
Condense
a)
A
b)
B
c)
C
d)
D
10.

Write in exponential form.

a)

A

b)

B

c)

C

d)

D

11.
a)
A
b)
B
c)
C
d)
D
12.
a)
A
b)
B
c)
C
d)
D
13.
a)
A
b)
B
c)
C
d)
D
14.
log88
a)
8
b)
-8
c)
1
d)
0
15.
8log8x
a)
0
b)
1
c)
x
d)
8
16.
a)
0
b)
1
c)
-3
d)
3
17.
a)
5log6(a) + 6log6(c) − 30log6(b)
b)
log6(a) + 6log6(c) − 5log6(b)
c)
6log6(a) − 6log6(c) − 30log6(b)
d)
6log6(a) + 6log6(c) − 30log6(b)
18.
a)
24log(u) - log(v)
b)
24log(u) + 6log(v)
c)
4log(u) + 6log(v)
d)
4log(u) - 6log(v)
19.
a)
log (xy3)
b)
log (x− y3)
c)
log (x6/y3)
d)
log (x6 + y3)
20.
Evaluate logb(b)
a)
-1
b)
0
c)
1
d)
b
21.
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
22.
Simplify eln(x)
a)
0
b)
1
c)
x
d)
8
23.
Simplify log443x
a)
3x
b)
3
c)
4
d)
43x
24.
The common logarithm has what base?
a)
10
b)
0
c)
e
d)
-e
25.
Rewrite logb(xn)
a)
nlogbx
b)
(logbx)n
c)
xnlogbx
d)
logb(xn)
26.
Write the expression as a single logarithm.   Then simplify if possible.
log53 + log56 + log59
a)
log569
b)
log556
c)
log5162
d)
log598
27.

Condense: log26+log23=

a)

log218

b)

log22 = 1

c)

log23

d)

log29

28.
Logarithms are the inverse of ___________.
a)
Trees
b)
Quadratics
c)
Square
d)
Exponential
29.
Write as a single log: log 12 + 2 log x
a)
log (12 + 2x)
b)
log (14x)
c)
log (12 * 2x)
d)
log (12x2)
30.

log (2 * 3) = ?

a)

log 2 + log 3

b)

log 2 * log 3

c)

log 2 - log 3

d)

log 5

31.

log (2 / 3) = ?

a)

log 2 + log 3

b)

log 2 / log 3

c)

log 2 - log 3

d)

2/3 * log 1

32.

log (32) =?

a)

log 6

b)

2 log 3

c)

log2 3

d)

log3 2

33.
When a logarithm has division inside of it, it expands using ________________.
a)
Addition
b)
Subtraction
c)
Multiplication
d)
Division
34.
10 log65+2log612
a)
log6(1210*52)
b)
log6(52/1210)
c)
log6(122*510)
d)
log6(55/122)
35.
2 log x-6 log y
a)
log(y2x6)
b)
log(x3/y2)
c)
log(x2/y6)
36.
The common logarithm has what base?
a)
10
b)
0
c)
e
d)
-e
37.
Rewrite 34 = 81 in logarithmic form.
a)
log34 = 81
b)
log813 = 4
c)
log381 = 4
d)
log481 = 3
38.
Expand.
a)
1/3 log x + log y + log z
b)
1/3 log x + 1/3 log y + 1/3 log z
c)
1/3 log x - 1/3 log y - 1/3 log z
d)
3 log x + 3 log y + 3 log z
39.
Write the expression as a single logarithm.   Then simplify if possible.
log 6 - log 3 + 2 log 7
a)
log 98
b)
log 78
c)
log 56
d)
log 45
40.
Logarithmic functions are the inverse of...
a)
Linear Functions
b)
Exponential Functions 
c)
Quadratic Functions 
d)
Polynomial Functions 
41.

Simplify.

10log125

a)

125

b)

12.5

c)

1250

d)

log125

42.
Evaluate log9(9)
a)
-1
b)
1
c)
0
d)
9
43.
Evaluate logb(b)
a)
-1
b)
0
c)
1
d)
b
44.
Simplify eln(x)
a)
0
b)
1
c)
x
d)
8
45.
Simplify 7log7(2x)
a)
0
b)
2x
c)
2
d)
1