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WorksheetsProperties 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
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 (a5 + b25)
b)
log (a5 − 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 (x6 − 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
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
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
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
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