Free Printable Expand / Condense Logarithms Review

1.

Which is better?

a)

cats

b)

birds

c)

goats

d)

DOGS!

2.

In the equation log₉729=3 , what is the base?

a)

9

b)

729

c)

3

3.

In the equation ln 3 = 1.1 , what is the base?

a)

3

b)

1.1

c)

e

d)

10

4.

In the equation log₈ 64 = 2 , what is the exponent?

a)

8

b)

64

c)

2

5.

What is the base for the common logarithm, when no base is written?

a)

1

b)

0

c)

e

d)

10

6.

Which of these is the exponential form of ln (0.7) = 2 ?

a)

10^0.7 = 2

b)

e^0.7=2

c)

e² = 0.7

d)

10² = 0.7

7.

Rewrite log_vn = a in exponential form.

a)

v^a = n

b)

n^a = v

c)

vⁿ = a

d)

aⁿ = v

8.

Write in exponential form.
log₂32 = 5

a)

2^-5 = 32

b)

2³² = 5

c)

2⁵ = 32

d)

32⁵ = 2

9.

Rewrite as an exponential equation:

log(10,000)=4.

a)

e⁴=10,000

b)

4^10,000=10

c)

10⁴=10,000

d)

0⁴=10

10.

Write the equation in logarithmic form.

$4^4=256$

a)

$\log_4\ 4\ =\ 256$

b)

$\log_{256}\ 4\ =\ 4$

c)

$\log_4\ 256\ =\ 4$

d)

$\log\ 4\ =\ 256$

11.

The college basketball team that should be my favorite is...

a)

GONZAGA!

b)

Villanova

c)

Kentucky

d)

UCLA

12.

Write the equation in logarithmic form.

$8^{3\ }=\ 512$

a)

$\log_38=512$

b)

$\log_8\ 512\ =\ 3$

c)

$\log_8\ 3=512$

d)

$\log_3\ 512\ =\ 8$

13.

Write in logarithmic form.
2^-4 = ¹/₁₆

a)

log₂(¹/₁₆) = -4

b)

log_-4(¹/₁₆) = 2

c)

log_-4 2 = ¹/₁₆

d)

log₂(-4) = ¹/₁₆

14.

Which of the following illustrates the Product Property of Logarithms

a)

log₃(x) ⋅ log₃(y) = log₃(x+y)

b)

log₃(x) ⋅ log₃(y) = log₃(xy)

c)

log₃(x) + log₃(y) = log₃(xy)

15.

Which of the following illustrates the Quotient Property of Logarithms

a)

log₄(x ÷ y) = log₄(x) - log₄(y)

b)

log₄(x ÷ y) = log₄(x) ÷ log₄(y)

c)

log₄(x - y) = log₄(x) ÷ log₄(y)

16.

Expand $\log_4\left(x^5y^2\right)$

a)

$10\log_4\left(x\ +y\right)$ 1

b)

$5\log_4x+2\log_4y$

c)

$5\log_9x+2\log_9y$

d)

$\log_4\left(5x+2y\right)$

17.

$Expand\ \log_5\left(xy^5\right)^2$

a)

$2\log_5x\ +10\log_5y$

b)

$10\left(\log_5x\ +\log_5y\right)$

c)

$10\log_5x\ +10\log_5y$

d)

$10\log_5x\ +2\log_5y$

18.

Expand
$\log_2\ \left(\frac{8x^3}{2y}\right)$

a)

$2+3\log_2x-\log_2y$

b)

$4+3\log_2x-\log_2y$

c)

$3\log_2x-\log_2y$

d)

$3\log_2x-3\log_2y$

19.

Expand the Log completely and simplify if possible. $\log_{ }\left(\frac{\sqrt{x}}{z^5y}\right)$

a)

$\frac{1}{2}\log x\ -5\log z-\log y$

b)

$\log\ x^{\frac{1}{2}\ }-\log\ z^5+\log\ y$

c)

$\log\ \sqrt{x}-\log z^5+y^{ }$

d)

$10\log\ x-z+y$

20.

Expand. (Be careful with the order of the answer choices, they are at random.)

a)

A

b)

B

c)

C

d)

D

21.

Expand the following: $\log_24g$

a)

$\log_24\times\log_2g$

b)

$\log_24+\log_2g$

c)

$\log_24-\log_2g$

d)

$\frac{\log_24}{\log_2g}$

22.

Expand the following: $\log\frac{n}{m}$

a)

$n\log m$

b)

$\log n+\log m$

c)

$\log n-\log m$

d)

$\frac{\log n}{\log m}$

23.

Expand the following: $\log_5\left(\frac{4xy}{z}\right)$

a)

$\log_54x+\log_5y-\log_5z$

b)

$\log_54+\log_5x+\log_5y-\log_5z$

c)

$\log_54xy-\log_5z$

d)

$\frac{\log_54xy}{\log_5z}$

24.

Expand the following: $\log_2\frac{x}{6y}$

a)

$\frac{\log_2x}{\log_26y}$

b)

$\log_2x+\log_26y$

c)

$\log_2x-\log_26-\log_2y$

d)

$\log_2x-\log_26+\log_2y$

25.

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

a)

5lnx + ln2y

b)

lnx5y2

c)

5lnx + 2lny

d)

5lnx - 2lny

26.

The best Algebra 2 teacher at GPHS is ...

a)

Ms. Cazares

b)

Mr. Creed

c)

Ms. Trujillo

d)

Mr. Derr

e)

Ms. Eaton

27.

Condense $15\ \log_5a\ +3\ \log_5b$

a)

$15\log_5ab$

b)

$\log_5\left(a^{15}b^3\right)$

c)

$\log_5\left(b^{15}a^3\right)$

d)

$45\log_5\left(ab\right)$

28.

$4\log_4u-6\log_4v$ Condense

a)

$\log_4\left(\frac{u}{v}\right)^{24}$

b)

$\log_4\left(\frac{u^6}{v^4}\right)^{ }$

c)

$\log_4\left(\frac{u^4}{v^6}\right)^{ }$

d)

$\log_4\left(\frac{v^6}{u^4}\right)^{24}$

29.

Condense into a single log:

\log_320-\log_35

a)

$\log_315$

b)

$\log_34$

c)

$\log_3100$

d)

$\log_3\frac{1}{4}$

30.

Condense into a single log:

\log_65+\log_62-\log_63

a)

$\log_67$

b)

$\log_64$

c)

$\log_6\frac{10}{3}$

31.

Condense into a single log:

\log_2x+\log_27-2\log_26

a)

$\log_2\left(\frac{14x}{6}\right)$

b)

$\log_2\left(\frac{7x}{36}\right)$

c)

$\log_2\left(\frac{7x}{12}\right)$

32.

Condense into a single log:

2\log7+5\log x-2\log5

a)

$\log\left(\frac{49x^5}{25}\right)$

b)

$\log\left(\frac{49x^5}{10}\right)$

c)

$\log\left(\frac{14x^5}{25}\right)$

d)

$\log\left(\frac{14x^5}{10}\right)$

33.

Condense the expression to a single logarithm.

16 log u + 4 log v

a)

log(u¹⁶v⁴)

b)

log(u⁴v⁴)

c)

log(u¹⁶/v⁴)

d)

log 64uv

34.

Use logarithm properties to condense the expression 2log b + log d

a)

b²+ d

b)

log b²d

c)

log2b + logd

d)

log(2bd)

35.

Condense the Logarithm: $\log_4x+\log_4y$

a)

$4\log xy$

b)

$\log_4xy$

c)

$y\log_4x$

d)

$\log_4\ \frac{x}{y}$

36.

Condense

$24\ \log\ x\ -\ 6\ \log\ y$

a)

$\log\ \frac{x^{24}}{y^6}$

b)

$\log\ \frac{4x}{y}$

c)

$\log\ \frac{x^4}{y}$

d)

$\log\ \frac{24x}{6y}$

37.

Condense: ln5 + 3lnx - 2lny

a)

ln5x³/y²

b)

ln5x³y²

c)

ln5/x³y²

d)

ln5x/y

38.

Condense. (Be careful with the order of the answer choices, they are at random.)

a)

A

b)

B

c)

C

d)

D

39.

Condense. (Be careful with the order of the answer choices, they are at random.)

a)

A

b)

B

c)

C

d)

D

40.

The college I should attend is ...

a)

b)

c)

d)

Expand / Condense Logarithms Review

Total questions: 40

Worksheet time: 7hrs 31mins

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