Free Printable LOGS review

1.

Write as one logarithm. Simplify, if possible.
log₂800 - log₂100

a)

8

b)

3

c)

-3

d)

1

2.

Write as one logarithm. Simplify, if possible.
log₆3 + log₆2

a)

0

b)

log₆5

c)

log₆1

d)

1

3.

$\log25\ +\ \log\ 4$

a)

$\frac{1}{3}$

b)

2

c)

-2

4.

Solve for x
5^x = 17

a)

x = log₁₇5

b)

x = log 5 + log 17

c)

x = log₅17

d)

x = (log 5)/(log 17)

5.

Expand

a)

A

b)

B

c)

C

d)

D

6.

Expand

a)

A

b)

B

c)

C

d)

D

7.

Expand

a)

log₈x + log₈y + log₈z

b)

5log₈x + 5log₈y + 5log₈z

c)

log₈xy + 5log₈z

d)

log₈x + log₈y + 5log₈z

8.

Rewrite e^x = 9 using a logarithm

a)

ln x = 9

b)

ln 9 = x

c)

log_x e = 9

d)

log₉ x = e

9.

Solve the equation for x.

a)

32

b)

25

c)

1.66

d)

512

10.

Solve

14^4-6x= 11

(round to the nearest tenth)

a)

5

b)

0.5

c)

0.1

d)

1

11.

ln(9x-2)=ln(x+14)

a)

x=2

b)

x=.156

c)

x=-3

d)

x=0

12.

$4\log_2\left(2x+24\right)-17=-9$
Once you have isolated the log in the equation, what would be the next step?

a)

log both sides

b)

rewrite as an exponential

c)

nothing, you would not be able to solve it

d)

divide both sides by 2

13.

Expand $\ln\ x^5y^2$

a)

5lnx + ln2y

b)

lnx5y2

c)

5lnx + 2lny

d)

5lnx - 2lny

14.

Logarithmic functions are the inverse of...

a)

Linear Functions

b)

Exponential Functions

c)

Quadratic Functions

d)

Polynomial Functions

15.

Evaluate the log:

log₃(1/9) =

a)

1/2

b)

2

c)

-2

d)

3

16.

Solve the equation $17^{-9x}+4=34$

a)

$\frac{-\log_{17}\left(\frac{30}{17}\right)+1}{9}$

b)

$\frac{\log_{17}\left(\frac{17}{2}\right)+9}{17}$

c)

$\frac{\log_9\left(\frac{3}{34}\right)}{17}$

d)

$-\frac{\log_{17}30}{9}$

17.

Solve the equation $-6\cdot14^{\left(x+2\right)}=-94$

a)

No solution

b)

$\log_{14}\left(\frac{47}{3}\right)-2$

c)

$\frac{\log_6\left(\frac{47}{7}\right)-1}{2}$

d)

$\frac{\log_{14}\left(44\right)-1}{14}$

18.

Solve the equation $-6\cdot18^{\left(5r\right)}+7=0$

a)

$\frac{\log_613}{7}$

b)

$\frac{\log_{18}\left(\frac{6}{5}\right)}{7}$

c)

$\frac{\log_{18}\left(\frac{7}{6}\right)}{5}$

d)

$\frac{\log_{18}\left(\frac{13}{18}\right)}{5}$

19.

Evaluate: $15^0=x$

a)

No Solution

b)

1

c)

0

d)

15

20.

$2\left(7^x\right)=686$

What would you do first to solve?

a)

Rewrite $7^x$ in logarithmic form

b)

Multiply both sides by 2

c)

Take the square root of both sides

d)

Divide both sides by 2

21.

7ⁿ⁺¹⁰- 8 = 6

a)

-7.374

b)

-8.643

c)

-7.360

d)

-8.853

22.

Solve for x:
5 e^6x+3= 0.1

a)

-1.152

b)

0.232

c)

-3.077

d)

-0.854

23.

If $1,000 is invested at 16% interest, compounded continuously, for five years, what is the ending balance?

a)

$1,225,54

b)

$2,225.54

c)

$22,255.40

d)

$225.54

24.

Compounded Continuously an investment of $400 at a rate of 35% for 2 years

a)

$280

b)

$680

c)

$1,034.47

d)

$805.50

25.

Which function has a horizontal asymptote?

a)

exponential

b)

logarithm

c)

both

d)

neither

26.

Which function has a vertical asymptote?

a)

exponential

b)

logarithm

c)

both

d)

neither

27.

How are exponentials and logarithms related?

a)

They're cousins

b)

They're inverses

c)

They're not related

d)

They're reciprocals

28.

Classify the following graph.

a)

Exponential Growth

b)

Exponential Decay

c)

Logarithmic

d)

Rational

29.

What is the base?

a)

1

b)

5

c)

10

d)

3

30.

What is the domain of log(x)?

a)

(-∞, ∞)

b)

[0, ∞)

c)

(0, ∞)

d)

(∞, -∞)

31.

What is the range of log(x)?

a)

(-2, 4)

b)

(-∞, ∞)

c)

(-∞, 0)

d)

(∞, -∞)

32.

a)

A

b)

B

c)

C

d)

D

33.

Rewrite log_vn = a in exponential form.

a)

v^a = n

b)

n^a = v

c)

vⁿ = a

d)

aⁿ = v

34.

The common logarithm has what base?

a)

10

b)

0

c)

e

d)

-e

35.

Solve each equation. Round your answers to the nearest ten-thousandth.

a)

19.1474

b)

.9688

c)

.0971

d)

-9.0312

36.

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

a)

"e"

b)

Natural Logarithm (LN)

c)

Common Logarithm (Log)

d)

Natural Log, base "e"
LN_e

37.

Rewrite in exponential form:
ln(2) = x

a)

2^x= 10

b)

10² = x

c)

e^x= 2

d)

e² = x

38.

Riley invested $1,000 in savings bonds. If the bonds earn 6.75% interest compounded semi-annually, how much total will Riley earn in 15 years?

a)

$1,584.62

b)

$2,651.39

c)

$2,706.86

d)

$1,825.10

39.

Treasure won $3,000 from a radio contest. If she puts this money in a bank account that earns 2.9% interest compounded quarterly, how much total will she have in 10 years?

a)

$4915.59

b)

$3933.28

c)

$2979.81

d)

$4005.09

40.

To evaluate a logarithm statement log₉81, you think "9 to what power is 81".

a)

True, and it's 2

b)

False

LOGS review

Total questions: 40

Worksheet time: 2hrs 8mins

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