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Solving Logarithm and Exponential Equations

Total questions: 45

Worksheet time: 3hrs 39mins

Name
Class
Date
1.
Write as a single log: log 12 + 2 log x
a)
log (12 + 2x)
b)
log (14x)
c)
log (12 * 2x)
d)
log (12x2)
2.
Expand log6(5x3/y).
a)
log65x3-log6y
b)
log65+log6x3-log6y
c)
log65+3log6x-log6y
3.

Solve

a)

-3

b)

3

c)

1/3

d)

No solution

4.

Solve

a)

46/5

b)

5/46

c)

-46/5

d)

-5/46

5.
Solve for x.
log770=log7(10x-30)
a)
x=1
b)
x=2
c)
x=10
d)
x=-2
6.
9x=3x-6
a)
x=5
b)
x=-6
c)
x=0
d)
x=Does Not Exist
7.
ln(9x-2)=ln(x+14)
a)
x=2
b)
x=.156
c)
x=-3
d)
x=0
8.
9x+3=3x+17
a)
X=1
b)
x=5
c)
x=-2
d)
x=11
9.
102x=10000
a)
x=2
b)
x=.019
c)
x=7
d)
Does Not Exist
10.
5x=(1/125)
a)
x=3
b)
x=2
c)
x=-3
d)
x=-4
11.
logx27=3
a)
x=6
b)
x=-3
c)
x=2
d)
x=3
12.
a)

x = 2

b)

x = 29

c)

x = 7

d)

x = 32

13.

Solve the equation. Round your answer to the nearest ten-thousandth.

a)

-0.1505

b)

-0.1643

c)

-0.3466

d)

-0.1182

14.

Solve the equation. Round your answer to the nearest thousandth.

a)

152.684

b)

188.7698

c)

4.240

d)

8.009

15.

The first step to solve the following equation 8 + log 7 = 10 is...

a)

Rewrite exponentially

b)

Subtract 8 on both sides to isolate the log

c)

Divide by 7 on both sides

16.

What is the base in the equation

log 8 = 3?

a)

8

b)

10

c)

3

d)

1

17.
Change to Exponential Form:
log636 = 2
a)
26=36
b)
62=36
c)
362=6
d)
366=2
18.
Change to Logarithmic Form:
53 = 125
a)
log 5 125 = 3
b)
log 3 125 = 5
c)
log 5 3 =125
d)
log125 3 = 5
19.

Log with a base "e" (loge) is the same thing as...

a)

"e"

b)

Natural Logarithm (LN)

c)

Common Logarithm (Log)

d)

Normal Log (LN)

20.

Condense: log26+log23=

a)

log218

b)

log22 = 1

c)

log23

d)

log29

21.

Expand: log3(5x2y3)

a)

log35x2 +log3y3

b)

log35+log3x2 +log3y3

c)

log35log3x2log3y3

d)

log35+2log3x +3log3y

22.
The common logarithm has what base?
a)
10
b)
0
c)
e
d)
-e
23.
Expand the logarithm
log10 7x
a)
(log10 7)(log10 x)
b)
log10 7 + log10 x
c)
7log10 x
d)
xlog10 7
24.

Solve: log2(x + 2) + log2(x)= 3

a)

-4, 2

b)

4; -2 is extraneous

c)

2; -4 is extraneous

d)

1; -3 is extraneous

25.
Solve for x.
5x = 1
a)
0
b)
-1
c)
2
d)
1
26.
ln(eW)
a)
e
b)
W
c)
eW
d)
undefined
27.
Solve log5(4x-7) =log5(x+5).
a)
x=4
b)
x=-4
c)
x=3
d)
x=-2
28.
What would the change base look like for:
  log6 48
a)
log 8
b)
log 6/log 48
c)
log 48/log 6
d)
ln 8
29.
Evaluate logb(b)
a)
-1
b)
0
c)
1
d)
b
30.

Logarithms are the inverse of ___________.

a)

Trees

b)

Quadratics

c)

Squares

d)

Exponentials

31.
The natural logarithm has what base?
a)
10
b)
0
c)
e
d)
-e
32.
Which of the following represent the  a change of base for logx y using the natural log?
a)
ln x / ln y
b)
ln y / ln x
c)
log x / log y
d)
log y / log x
33.
log (-1) = 
a)
0.1
b)
.01
c)
all real numbers
d)
does not exist
34.

Simplify

a)

e

b)

0

c)

1

d)

-1

35.
Evaluate:
log554
a)
e
b)
10
c)
5
d)
4
36.
Write logb(xy) as two logs
a)
logbx+logby
b)
logbx-logby
c)
logbx*logby
d)
logbx/logby
37.
There are 3 apples on an apple tree. You take 2. How many do you have?
a)
2
b)
1
c)
3
d)
Bieber
38.
What belongs to you but others use it more than you do?
a)
Your name
b)
Your toys
c)
Your life
d)
Your phone
39.

Solve: log 6 - log 3x = -2

a)

.02

b)

200

c)

.03

d)

undefined

40.

Select the two basic strategies for solving Logarithms? (pick 2 answers)

a)

One to One Property

b)

Drop the logarithms and solve for x

c)

Inverse Property

d)

Use a calculator

41.

Logarithm functions are just exponential functions written a different way.

a)

True

b)

False

42.

Using Logarithms gives us a way to solve equations when the variable is the exponent.

a)

True

b)

False

43.

You cannot take the log of a negative number or 0.

a)

True

b)

False

44.

Expand:

a)

3log57x

b)

3log5x + log57

c)

log57 - 3log5x

d)

3log5x - log57

45.

Condense: log6 + 2logy - 5logx

a)

log6y/x

b)

log6/y2x5

c)

log6y2x5

d)

log6y2/x5

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