WorksheetsLogarithm and Exponential Equations/Expressions
Total questions: 20
Worksheet time: 40mins
Name
Class
Date
1.
Rewrite in exponential form:
log (x) = ¼
log (x) = ¼
a)
x1/4 = 1
b)
1x =¼
c)
101/4 = x
d)
10x = ¼
2.
Rewrite in exponential form:
ln(2) = x
ln(2) = x
a)
2x = 10
b)
102 = x
c)
ex = 2
d)
e2 = x
3.
Evaluate.
log381
log381
a)
4
b)
1/4
c)
-4
d)
-1/4
4.
Write as one logarithm. Simplify, if possible.
log63 + log62
log63 + log62
a)
0
b)
log65
c)
log61
d)
1
5.
Rewrite logpt = m in exponential form.
a)
pt = m
b)
tm = p
c)
mt = p
d)
pm = t
6.
Condense into a single logarithm.
a)
A
b)
B
c)
C
d)
D
7.
Condense into a single logarithm.
a)
A
b)
B
c)
C
d)
D
8.
Write as a single logarithm
a)
log xyz3
b)
log (xy/z3)
c)
log x + log y + log z3
d)
log x3y3z3
9.
Solve the equation.
a)
A
b)
B
c)
C
d)
D
10.
What is the value of ln(e7)
a)
2.718...
b)
1
c)
7
d)
Does not exist
11.
Solve the following equation for x. Round your solution to two decimal places.
ln2x - ln41 = 2
ln2x - ln41 = 2
a)
x = 0.36
b)
x = 151.48
c)
x = 41
d)
None of these are solutions
12.
Solve for x:
e2x = 11
e2x = 11
a)
x = (LN 11)/2
b)
x = 2loge11
c)
x = 2eLOG 11
d)
x = LN (11/2)
13.
log232=3x
a)
5/3
b)
3/5
c)
5
d)
3
14.
log4(3x-1)=log4(2x+3)
a)
4
b)
3
c)
1
d)
8
15.
logx1000=3
a)
1
b)
10
c)
30
d)
3
16.
log8(4x+4)=2
a)
15
b)
12
c)
10
d)
3
17.
lnx = -3
a)
8.1548
b)
-8.1548
c)
0.0498
d)
-0.0498
18.
Solve for x:
42x + 1 = 17
42x + 1 = 17
a)
x = 1
b)
x = -1
c)
x = 2
d)
x = -2
19.
Solve for x:
23x - 1 = 32
a)
0
b)
-1
c)
5/3
d)
2
20.
Solve:
log (4x − 5) = log (2x − 1)
log (4x − 5) = log (2x − 1)
a)
0
b)
1
c)
2
d)
3
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