Quiz about Basic Properties of Logarithms Review

Question 1

Write in logarithmic form.
5² = 25

Accepted Answer

log₅25 = 2

Answer

log₅2 = 25

Answer

log₂25 = 5

Answer

log₂₅5 = 2

Question 2

Write in exponential form.
log₂32 = 5

Accepted Answer

25 = 32

Answer

2-5 = 32

Answer

232 = 5

Answer

325 = 2

Question 3

Rewrite log_vn = a in exponential form.

Accepted Answer

va = n

Answer

na = v

Answer

vn = a

Answer

an = v

Question 4

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

Accepted Answer

log₂(¹/₁₆) = -4

Answer

log_-4(¹/₁₆) = 2

Answer

log_-4 2 = ¹/₁₆

Answer

log₂(-4) = ¹/₁₆

Question 5

Condense the expression to a single logarithm.

16 log u + 4 log v

Accepted Answer

log(u¹⁶v⁴)

Answer

log(u⁴v⁴)

Answer

log(u¹⁶/v⁴)

Answer

log 64uv

Question 6

Rewrite as an exponential equation:

log(10,000)=4.

Accepted Answer

10⁴=10,000

Answer

e⁴=10,000

Answer

4^10,000=10

Answer

04=10

Question 7

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

Accepted Answer

log b2d

Answer

b2 + d

Answer

log2b + logd

Answer

log(2bd)

Question 8

What type of functions are logarithms the inverse of?

Accepted Answer

Exponential functions

Answer

Quadratic functions

Answer

Linear functions

Answer

Radical functions

Question 9

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

Accepted Answer

9

Answer

729

Answer

3

Question 10

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

Accepted Answer

1/32

Answer

2

Answer

32

Answer

-5

Question 11

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

Accepted Answer

2

Answer

8

Answer

64

Question 12

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

Accepted Answer

e

Answer

3

Answer

1.1

Answer

10

Question 13

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

Accepted Answer

10

Answer

1

Answer

0

Answer

e

Question 14

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

Accepted Answer

e² = 0.7

Answer

100.7 = 2

Answer

e0.7 =2

Answer

102 = 0.7

Question 15

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

Accepted Answer

4

Answer

1/4

Answer

32

Answer

1/32

Question 16

Solve for x in the equation log₁₃ x = 2

Accepted Answer

169

Answer

8,192

Answer

26

Answer

6.5

Question 17

Solve for x in the equation log₅625 = x

Accepted Answer

4

Answer

-4

Answer

125

Answer

-5

Question 18

Solve for x in the equation ln 1 = x

Accepted Answer

0

Answer

e

Answer

1

Answer

10

Question 19

Solve for x in the equation log x = 4

Accepted Answer

10,000

Answer

40

Answer

256

Answer

10

Question 20

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

Accepted Answer

-1.3

Answer

-2

Answer

1.7

Answer

0.6

Question 21

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

Accepted Answer

$$3\ln x\ +\ln y$$

Answer

$$3\ln x-\ln y$$

Answer

$$3\ln x+3\ln y$$

Answer

$$3\ln x-3\ln y$$

Question 22

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 23

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

Accepted Answer

initial value

Answer

common ratio

Answer

number of months

Answer

total number of bacteria

Question 24

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

Accepted Answer

common ratio

Answer

initial value

Answer

number of months

Answer

total number of bacteria

Question 25

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

Accepted Answer

number of months

Answer

initial value

Answer

common ratio

Answer

total number of bacteria

Question 26

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

Accepted Answer

total number of bacteria

Answer

initial value

Answer

common ratio

Answer

number of months

Question 27

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

Accepted Answer

Answer

Answer

Answer

Basic Properties of Logarithms Review

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