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WorksheetsProperties Of Logarithms
Total questions: 72
Worksheet time: 3hrs 56mins
Name
Class
Date
1.
Write the following equation in exponential form:
log232 = 5
log232 = 5
a)
25 = 32
b)
232 = 5
c)
52 = 32
d)
322 = 5
2.
log2(x + 5) = 3
a)
3
b)
4
c)
5
d)
6
3.
log2(x + 2) + log2x = 3
a)
-4, 2
b)
-2, 4
c)
2
d)
1
4.
4(x-2)= 64(x+1)
a)
-2/5
b)
-5/2
c)
7/2
d)
2/7
5.
Write logb(xy) as two logs
a)
logbx+logby
b)
logbx-logby
c)
logbx*logby
d)
logbx/logby
6.
Condense: log26+log23=
a)
log218
b)
log22 = 1
c)
log23
d)
log29
7.
Expand
a)
A
b)
B
c)
C
d)
D
8.
a)
A
b)
B
c)
C
d)
D
9.
Condense
a)
logxyz3
b)
log(xy/z3)
c)
logx+logy+logz3
d)
logx3y3z3
10.
Expand
a)
log8x+log8y+log8z
b)
5log8x+5log8y+5log8z
c)
log8xy+5log8z
d)
log8x+log8y+5log8z
11.
Write logb(x/y) as two logs
a)
logbx-logby
b)
logbx+logby
c)
logbx*logby
d)
logbx/logby
12.
Evaluate logb(b)
a)
-1
b)
0
c)
1
d)
b
13.
Rewrite logb(xn)
a)
nlogbx
b)
(logbx)n
c)
xnlogbx
d)
logb(xn)
14.
log(10 - 4a) = log(-3a + 8)
a)
-1
b)
2
c)
No Solution
d)
-13/3
15.
log(- 4x - 6) - log(6) = log(64)
a)
-195/2
b)
-14/3
c)
-2
d)
No Solution
16.
log(5) + log(8-5x) = 1
a)
6/5
b)
-195/3
c)
-7/3
d)
4
17.
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
18.
Write as a single log: log 12 + 2 log x
a)
log (12 + 2x)
b)
log (14x)
c)
log (12 * 2x)
d)
log (12x2)
19.
Condense: log26+log23=
a)
log218
b)
log22 = 1
c)
log23
d)
log29
20.
Write logb(xy) as two logs
a)
logbx+logby
b)
logbx-logby
c)
logbx*logby
d)
logbx/logby
21.
Expand
a)
A
b)
B
c)
C
d)
D
22.
Condense
a)
logxyz3
b)
log(xy/z3)
c)
logx+logy+logz3
d)
logx3y3z3
23.
Expand log3(9x2)
a)
3+2log3x
b)
log39+2log3x
c)
2+2log3x
d)
log9+2logx
24.
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
25.
Rewrite 34 = 81 in logarithmic form.
a)
log34 = 81
b)
log813 = 4
c)
log381 = 4
d)
log481 = 3
26.
Simplify 8log8x
a)
0
b)
1
c)
x
d)
8
27.
Simplify eln(x)
a)
0
b)
1
c)
x
d)
8
28.
Simplify 7log7(2x)
a)
0
b)
2x
c)
2
d)
1
29.
Condense
a)
A
b)
B
c)
C
d)
D
30.
Expand
a)
A
b)
B
c)
C
d)
D
31.
Condense
a)
A
b)
B
c)
C
d)
D
32.
Expand
a)
A
b)
B
c)
C
d)
D
33.
Condense
a)
log8(x6)/log8(y3)
b)
log8(x6/y3)
c)
log8(x/y3)
d)
log8(x6y3)
34.
Write the following equation in exponential form:
log232 = 5
log232 = 5
a)
25 = 32
b)
232 = 5
c)
52 = 32
d)
322 = 5
35.
Rewrite 34 = 81 in logarithmic form.
a)
log34 = 81
b)
log813 = 4
c)
log381 = 4
d)
log481 = 3
36.
6x+2 = 18
a)
0.3869
b)
-0.3869
c)
1.3869
d)
-1.7594
37.
Solve:
62x + 1 = 5x
62x + 1 = 5x
a)
x = -1
b)
x = -.0509
c)
x = -2.4702
d)
x = -.9076
38.
Evaluate logb(1)
a)
0
b)
1
c)
-1
d)
b
39.
Evaluate blogb(x)
a)
x
b)
b
c)
1
d)
0
40.
Rewrite logb(a) with base a
a)
1/(logab)
b)
-logba
c)
1/(logba)
d)
-logab
41.
logbx=y iff _______
a)
by=x
b)
logby=x
c)
bx=y
d)
logxb=y
42.
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
43.
Write as a single log: log 12 + 2 log x
a)
log (12 + 2x)
b)
log (14x)
c)
log (12 * 2x)
d)
log (12x2)
44.
Use a property of logs to write this in another way.
x log7 y
x log7 y
a)
log yx
b)
log7 yx
c)
log7 xy
d)
log7 yx
45.
Write logb(xy) as two logs
a)
logbx+logby
b)
logbx-logby
c)
logbx*logby
d)
logbx/logby
46.
Simplify log443x
a)
3x
b)
3
c)
4
d)
43x
47.
Expand log6(5x3/y).
a)
log65x3-log6y
b)
log65+log6x3-log6y
c)
log65+3log6x-log6y
48.
a)
6log8(xyz)
b)
log8(x) - log8(y) - 6log8(z)
c)
log8(x) + log8(y) - log8(z)
d)
log8(x) + log8(y) + 6log8(z)
49.
Write as a single log: log 12 + 2 log x
a)
log (12 + 2x)
b)
log (14x)
c)
log (12 * 2x)
d)
log (12x2)
50.
Evaluate blogb(x)
a)
x
b)
b
c)
1
d)
0
51.
Condense
a)
A
b)
B
c)
C
d)
D
52.
a)
log (a5 + b25)
b)
log (a5 − b25)
c)
log (ab25)
d)
log (a5/b25)
53.
Condense
a)
logxyz3
b)
log(xy/z3)
c)
logx+logy+logz3
d)
logx3y3z3
54.
a)
log(x) + log(z) + 4log(y)
b)
3log(x) − log(z) − 4log(y)
c)
3log(x) + log(z) + 4log(y)
d)
log(x) − 4log(z) − 3log(y)
55.
Expand
a)
6log8v-2log8u
b)
6log8u-2log8v
c)
3log8u-2log8v
d)
6log8u+2log8v
56.
a)
log(x) + log(z) + 4log(y)
b)
3log(x) − log(z) − 4log(y)
c)
3log(x) + log(z) + 4log(y)
d)
log(x) − 4log(z) − 3log(y)
57.
Write as one logarithm. Simplify, if possible.
log39 + log327
log39 + log327
a)
-1
b)
5
c)
4
d)
1
58.
Write as one logarithm. Simplify, if possible.
log63 + log62
log63 + log62
a)
0
b)
log65
c)
log61
d)
1
59.
Write as one logarithm. Simplify, if possible.
log5125 - log525
log5125 - log525
a)
1
b)
0
c)
5
d)
-1
60.
Evaluate.
3 log24
3 log24
a)
3
b)
6
c)
2
d)
4
61.
log(10R)
a)
10
b)
1
c)
R
d)
10R
62.
Evaluate.
log6(1/216)
log6(1/216)
a)
3
b)
1/3
c)
-1/3
d)
-3
63.
Solve for x:
log4 x = 3
log4 x = 3
a)
4
b)
12
c)
32
d)
64
64.
Condense, 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
65.
Use the change of base formula and your calculator to approximate the log.
a)
A
b)
B
c)
C
d)
D
66.
Logarithms are the inverse of ___________.
a)
Trees
b)
Quadratics
c)
Square
d)
Exponential
67.
12 log u + 3 log v
a)
log(v3u12)
b)
log(vuw4)
c)
log(u3/v12)
68.
24 log43-6log48
a)
log4(34/8)
b)
log4(86*324)
c)
log4(324/86)
69.
10 log65+2log612
a)
log6(1210*52)
b)
log6(52/1210)
c)
log6(122*510)
d)
log6(55/122)
70.
2 log x-6 log y
a)
log(y2x6)
b)
log(x3/y2)
c)
log(x2/y6)
71.
a)
0
b)
1
c)
-3
d)
3
72.
Rewrite the equation in exponential form:
logvn = a
logvn = a
a)
va = n
b)
na = v
c)
vn = a
d)
an = v
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