Free Printable Algebra 2 Logarithm Review

1.

Write in logarithmic form.
5² = 25

a)

log₅2 = 25

b)

log₂25 = 5

c)

log₂₅5 = 2

d)

log₅25 = 2

2.

Write in exponential form.
log₂32 = 5

a)

2^-5 = 32

b)

2³² = 5

c)

2⁵ = 32

d)

32⁵ = 2

3.

Rewrite log_vn = a in exponential form.

a)

v^a = n

b)

n^a = v

c)

vⁿ = a

d)

aⁿ = v

4.

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

5.

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

6.

a)

log (xy³)

b)

log (x⁶− y³)

c)

log (x⁶/y³)

d)

log (x⁶ + y³)

7.

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

8.

Use logarithm properties to condense the expression log b² + log d

a)

b²+ d

b)

log b²d

c)

log2b + logd

d)

log(2bd)

9.

What type of functions are logarithms the inverse of?

a)

Quadratic functions

b)

Linear functions

c)

Radical functions

d)

Exponential functions

10.

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

a)

9

b)

729

c)

3

11.

In the equation log₂ (1/32) = -5 , what is the argument?

a)

2

b)

1/32

c)

32

d)

-5

12.

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

a)

8

b)

64

c)

2

13.

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

a)

3

b)

1.1

c)

e

d)

10

14.

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

a)

1

b)

0

c)

e

d)

10

15.

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

16.

Solve for x in the equation log_x (1/16) = -2

a)

1/4

b)

4

c)

32

d)

1/32

17.

Solve for x in the equation log₁₃ x = 2

a)

8,192

b)

169

c)

26

d)

6.5

18.

Solve for x in the equation log₅625 = x

a)

4

b)

-4

c)

125

d)

-5

19.

Solve for x in the equation ln 1 = x

a)

e

b)

0

c)

1

d)

10

20.

Solve for x in the equation log x = 4

a)

40

b)

256

c)

10,000

d)

10

21.

Solve for x in the equation 4^x+3 = 10

a)

-2

b)

-1.3

c)

1.7

d)

0.6

22.

Use properties of logarithms to expand the expression $\ln\left(x^3y\right)$

a)

$3\ln x\ +\ln y$

b)

$3\ln x-\ln y$

c)

$3\ln x+3\ln y$

d)

$3\ln x-3\ln y$

23.

Which of these exponential equations can be solved with the Property of Equality?

a)

$8^{6x}=32^{x+7}$

b)

$9^x=18^{2x-3}$

c)

$15^{4x-1}=35^{x+1}$

d)

$3^{4x}=36^{5x-2}$

24.

In the exponential function to measure bacteria growth over several months, $f\left(x\right)=6\cdot3^x$ , what does the 6 represent?

a)

initial value

b)

common ratio

c)

number of months

d)

total number of bacteria

25.

In the exponential function to measure bacteria growth over several months, $f\left(x\right)=6\cdot3^x$ , what does the 3 represent?

a)

initial value

b)

common ratio

c)

number of months

d)

total number of bacteria

26.

In the exponential function to measure bacteria growth over several months, $f\left(x\right)=6\cdot3^x$ , what does the x represent?

a)

initial value

b)

common ratio

c)

number of months

d)

total number of bacteria

27.

In the exponential function to measure bacteria growth over several months, $f\left(x\right)=6\cdot3^x$ , what does the f(x) represent?

a)

initial value

b)

common ratio

c)

number of months

d)

total number of bacteria

28.

Solve for x in the equation $5^{4x-1}=125^{x+3}$

a)

x=10

b)

x=4/3

c)

x=3/4

d)

x=11/5

Algebra 2 Logarithm Review

Total questions: 28

Worksheet time: 36mins

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