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Logs! Logs! Logs!

Total questions: 66

Worksheet time: 4hrs 52mins

Name
Class
Date
1.

Change to Exponential Form:

log636 = 2

a)

26=36

b)

62=36

c)

362=6

d)

366=2

2.

Rewrite 34 = 81 in logarithmic form.

a)

log34 = 81

b)

log813 = 4

c)

log381 = 4

d)

log481 = 3

3.

Evaluate on calculator log41 =

a)

0

b)

1

c)

4

d)

1.4

4.

Change y = ax into log form.

a)

x = logay

b)

y = logax

c)

x = logya

d)

y = log a

5.
Write in logarithmic form.
52 = 25
a)
log52 = 25
b)
log225 = 5
c)
log255 = 2
d)
log525 = 2
6.

Convert to exponential form and solve for x:

log2(x + 5) = 3

a)

3

b)

4

c)

5

d)

6

7.
Solve:
3x-1 = 81
a)
5
b)
6
c)
9
d)
10
8.
Solve:
log (4x − 5) = log (2x − 1) 
a)
0
b)
1
c)
2
d)
3
9.

Evaluate the log on calculator:

log3(1/9) =

a)

1/2

b)

2

c)

-2

d)

3

10.

Solve log5(4x-7)=log5(x+5)

a)

3

b)

12

c)

4

d)

7

11.

Solve: log5(x+7)=log5(2x+3)

a)

x=5

b)

x=10/3

c)

x=4

d)

x=-4

12.

Solve: 72x+6=49

a)

x=2

b)

x=-2

c)

x=0

d)

x=-4

13.
log (x) + log (x) = log (25)
a)
-5, 5
b)
5
c)
-5
d)
25
14.
Write as a single log: log 12 + 2 log x
a)
log (12 + 2x)
b)
log (14x)
c)
log (12 * 2x)
d)
log (12x2)
15.

Simplify into a single logarithm

6 log8 x - 3 log8 y

a)

log8(x6)/log8(y3)

b)

log8(x6/y3)

c)

log8(x/y3)

d)

log8(x6y3)

16.

What kind of function is this graph?

a)

Exponential Growth

b)

Exponential Decay

c)

Linear

d)

Cubic

17.

log 2 + log 3

a)

log 6

b)

log 5

c)

log 2/3

d)

log 1

18.

log 2 - log 3

a)

log (2/3)

b)

log 2 / log 3

c)

log -1

d)

log 6

19.

log 32 =?

a)

log 6

b)

2 log 3

c)

log2 3

d)

log3 2

20.
Change to Logarithmic Form:
122 = 144
a)
log 2 144 = 12
b)
log 12 144 = 2
c)
log 12 2 = 144
d)
log 2 12 = 144
21.

Simplify into a single logarithm: log26+log23=

a)

log218

b)

log22 = 1

c)

log23

d)

log29

22.
You drink a beverage with 120 mg of caffeine. Each hour, the caffeine in your system decreases by about 12%. How long until you have 10mg of caffeine? 
a)
19 to 20 hours
b)
10 to 20 hours
c)
15 to 16 hours
d)
5 to 6 hours
23.

Which equation matches this situation? You put $15 in a savings account that earns 35% interest

a)

y = 15(35)x

b)

y = 15(1.35)x

c)

y = 15(0.35)x

d)

y = 35(1.15)x

24.

Rewrite log231 as base 10 using the change of base rule.

a)

log 2 / log 31

b)

log 2/31

c)

log 31 / log 2

d)

log 31/ 2

25.
Logarithmic functions are the inverse of...
a)
Linear Functions
b)
Exponential Functions 
c)
Quadratic Functions 
d)
Polynomial Functions 
26.

Rewrite 42 = x in log form

a)

logx 4 = 2

b)

log4 2 = x

c)

log2 x = 4

d)

log4 x = 2

27.

What is the asymptote of y = 2x ?

a)

y = 0

b)

x = 0

28.

What is the asymptote of y = 2x - 3

a)

y = 0

b)

y = -3

c)

x = 0

d)

x = -3

29.

What is the asymptote of y = log2x ?

a)

y = 0

b)

x = 0

30.

What is the asymptote of y = log2x - 3

a)

y = 0

b)

y = -3

c)

x = 0

d)

x = -3

31.

The asymptote of y = 2x + 4 will shift...

a)

up four to y = 4

b)

down four to y = -4

c)

not shift at all and remain y = 0

32.

The asymptote of y = log2(x + 2) will shift...

a)

right two to x = 2

b)

left two to x = -2

c)

not shift and remain x = 0

33.
The foundation of your house has about 1,200 termites. The termites grow at a rate of about 2.4% per day. How long until the number of termites doubles?
a)
29 to 30 years
b)
23 to 24years
c)
15 to 16 years
d)
19 to 20 years
34.

There are 4,000 mosquitoes at the beginning of the summer. The population of mosquitoes is expected to grow at a rate of 25% a month. How many mosquitoes will there be after 4 months?

a)

9766

b)

9006

c)

9765

d)

5433

35.

You buy a new computer for $2100. The computer depreciates in value by 50% annually. How much is it worth after 2 years.

a)

225

b)

325

c)

425

d)

525

36.

Which of the following is the sketch of the graph of y = -log3 (x+5) ?

a)
b)
c)
d)
37.

log7z+log7b

a)

log7(z*b)

b)

logz*b(7)

c)

logz(b*7)

d)

logb(z*7)

38.
Condense: log16 + log2 - log8
a)
log4
b)
log8
c)
log10
d)
log24
39.

Solve for x: log3(x+4) = log3(5x)

a)

x=5

b)

x=4

c)

x=1

d)

x=3

40.
The population of a small coastal resort town, currently 3400, grows at a rate of 3% per year.  This growth can be expressed by the exponential equation P = 3400(1+.03)x, where P is the population after t years.  Find the number of years it will take for the population to reach 10,000?
a)
20 years
b)
26 years
c)
30 years
d)
36 years
41.
Condense the following logarithm: 3 log2 x + 2 log2 y – 4 log2 z 
a)
log2 x3y2∕z4
b)
log2 x3y2z4
c)
log2 xyz9
d)
9log2 xyz
42.
a)
log8(a2/cb3)
b)
log8(ca2/b3)
c)
log8(a2cb3)
d)
log(a2 − c − b3) 
43.
a)
log5(x2z2y10)
b)
log5(z2y2x10)
c)
log(zy2x10)
d)
log5(z2 + y2 + x10)
44.
a)
log (xy3)
b)
log (x6 − y3)
c)
log (x6/y3)
d)
log (x6 + y3)
45.
a)
log (a5 + b25)
b)
log (a5 − b25)
c)
log (ab25)
d)
log (a5/b25)
46.
a)
log3(a36 − b6)
b)
log3(a36 + b6)
c)
log(a36b6)
d)
log3(a36/b6)
47.
Condense
a)
logxyz3
b)
log(xy/z3)
c)
logx+logy+logz3
d)
logx3y3z3
48.
Condense
a)
log8(x6)/log8(y3)
b)
log8(x6/y3)
c)
log8(x/y3)
d)
log8(x6y3)
49.
Solve: 98-x = 27x-3
a)
5
b)
-5
c)
1/5
d)
-1/5
50.
Solve for n:
23n = 4
a)
2
b)
3
c)
2/3
d)
4
51.

Use the change of base rule to rewrite this problem:

log364

a)

log(64)/log(3)

b)

log(3)/log(64)

52.

Use the change of base rule to rewrite this problem:

log575

a)

log(75)/log(5)

b)

log(5)/log(75)

53.

Use the change of base rule to rewrite this problem:

log6216

a)

log(6)/log(216)

b)

log(216)/log(6)

54.

Use the change of base rule to rewrite this problem:

log7729

a)

log(7)/log(729)

b)

log(729)/log(7)

55.

Use the change of base rule to rewrite this problem:

log216

a)

log(16)/log(2)

b)

log(2)/log(16)

56.

Use the change of base rule to rewrite this problem:

log864

a)

log(8)/log(64)

b)

log(64)/log(8)

57.

Use the change of base rule to rewrite this problem:

log5625

a)

log(625)/log(5)

b)

log(5)/log(625)

58.
Solve the equation for x.
a)
32
b)
25
c)
1.66
d)
512
59.

Who is playing in this year's Superbowl?

a)

Chiefs vs Eagles

b)

Chiefs vs 49ers

c)

Chiefs vs Patriots

d)

Chiefs vs Titans

60.

Who is performing in this year's Superbowl Half Time show?

a)

J Lo

b)

Bruno Mars

c)

Maroon 5

d)

Beyonce

61.

What number is this year's Superbowl?

a)

Super Bowl LIV

b)

Super Bowl LI

c)

Super Bowl L

d)

Super Bowl LV

62.

What city will the Super Bowl be held in?

a)

Atlanta, GA

b)

Miami, FA

c)

Denver, CO

d)

New Orleans, LA

63.

What number is this year's Superbowl?

a)

Super Bowl LIV

b)

Super Bowl LI

c)

Super Bowl L

d)

Super Bowl LV

64.

How many seats are there at arrowhead stadium?

a)

76,000

b)

500000000

c)

4

d)

100

65.

How many touchdowns did Patrick Mahomes have in the 2018-19 season?

a)

34

b)

29

c)

11

d)

50

66.

How many reviving yards did Travis Kelce have in the 2018-19 season ?

a)

1,189

b)

987

c)

1,336

d)

1,354

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