Quiz about Logarithmic Functions Graph and Properties

Question 1

Convert the log form to exponent form and find the value of x. $$\log_{10}(x)=2$$ .

Accepted Answer

100

Answer

10

Answer

1000

Answer

0.01

Question 2

Fill in the blank for the exponent form: $$10^2=100$$ .

Logarithmic Form: $$\log\ \left(\ 100\right)\ =\ -----$$

Accepted Answer

2

Answer

1

Answer

3

Answer

4

Question 3

Convert logarithm form to exponent form. $$\log_a(z)=c$$

Accepted Answer

$$a^c=z$$

Answer

$$z^a=c$$

Answer

$$ac=z$$

Answer

$$c^z=a$$

Question 4

Find the domain of the function: f(x) = log_3 (x + 5) - 2.

Accepted Answer

x > -5

Answer

y < 5

Answer

x < -5

Answer

y > -5

Question 5

Find the range of the function. $$\log_2(x-4)-3$$

Accepted Answer

All real numbers

Answer

x > 4

Answer

y > -4

Answer

y > -3

Question 6

$$f\left(x\right)=\log\left(x-6\right)+7$$ for What is the value of x, $$f(x)=0$$ ?

Accepted Answer

6

Answer

5

Answer

7

Answer

8

Question 7

What is the x intercept of the function $$f(x)=\log_5(x+1)-3$$ ?

Accepted Answer

(124, 0)

Answer

(0, -124)

Answer

(126, 0)

Answer

(-126, 0)

Question 8

What is the y intercept of the function $$f(x)=\log_5(x+1)-5$$ ?

Accepted Answer

(0, -5)

Answer

(1, 0)

Answer

(0, -1)

Answer

(-5, 0)

Question 9

Calculate the value of x. Given $$\log_3(x)=3$$

Accepted Answer

27

Answer

9

Answer

81

Answer

3

Question 10

Use properties of the logarithms to match the expressions: log(4x) = log4 + logx

Accepted Answer

Product Rule

Answer

Equality Rule

Answer

Quotient Rule

Answer

Power Rule

Question 11

Use properties of the logarithms to match the expressions: $$\log\left(\frac{7}{y}\right)=\log7-\log y$$

Accepted Answer

Quotient Rule

Answer

Equality Rule

Answer

Product Rule

Answer

Power Rule

Question 12

Use properties of the logarithms to match the expressions: $$\log(y^2)=2\log y$$

Accepted Answer

Power Rule

Answer

Equality Rule

Answer

Product Rule

Answer

Quotient Rule

Question 13

Use properties of the logarithms to match the expressions: If log(x) = log(y), then x=y

Accepted Answer

Equality Rule

Answer

Product Rule

Answer

Quotient Rule

Answer

Power Rule

Question 14

Use the properties of logarithms to find $$\log\left(5\right)^3$$

Accepted Answer

$$3\cdot\log(5)$$

Answer

$$\log(5\cdot3)$$

Answer

3 + log(5)

Answer

$$\log(5)^3$$

Question 15

Evaluate log_4 4123

Accepted Answer

123

Answer

124

Answer

1

Answer

4

Question 16

Evaluate $$e^{\ln60}$$

Accepted Answer

60

Answer

1

Answer

e

Answer

6

Question 17

Describe the transformation of the function log(x - 5) + 2.

Accepted Answer

up 2 units

Accepted Answer

right 5 units

Accepted Answer

reflect over x axis

Answer

down 2 units

Answer

left 5 units

Question 18

For the function (2log(x + 6) - 7), select all the transformations that apply:

Accepted Answer

Stretch vertically by a factor of 2, left 6 units, down 7 units

Answer

Stretch horizontally by a factor of 2, right 6 units, up 7 units

Answer

Reflect over x axis

Answer

Stretch vertically by a factor of 1/2

Question 19

Solve for x: $$\log(9x)=\log(12x+9)$$

Accepted Answer

x = -3

Answer

x = -1

Answer

x = 5

Answer

x = 0

Question 20

What is the value of x if ln e = x?

Accepted Answer

1

Answer

-2

Answer

2

Answer

-1

Question 21

Write log₂ 0.25 = -2 in exponential form

Accepted Answer

2-2 = 0.25

Answer

-22 = 0.25

Answer

-20.25 = 2

Answer

No correct answer

Question 22

Rewrite in exponential form:
ln(2) = x

Accepted Answer

ex = 2

Answer

2x = 10

Answer

102 = x

Answer

e2 = x

Question 23

Change to Exponential Form:
log₆36 = 2

Accepted Answer

62=36

Answer

26=36

Answer

362=6

Answer

366=2

Question 24

Convert 10^(x+5)=100 to logarithmic form.

Accepted Answer

log(100)=x+5

Answer

log₁₀₀=x+5

Answer

log(x+5)=100

Answer

log_(x+5)(100)=10

Question 25

Rewrite the exponential equation $$5^3 = 125$$ as a logarithmic equation.

Accepted Answer

$$\log_5 125 = 3$$

Answer

$$\log_3 125 = 5$$

Answer

$$\log_5 3 = 125$$

Answer

$$\log_{125} 5 = 3$$

Question 26

Rewrite the equation in logarithmic form: $$64^{\frac{1}{2}}=8$$ ?

Accepted Answer

$$\log_{64}\ 8=\frac{1}{2}$$

Answer

$$\log_8\ 64=\frac{1}{2}$$

Answer

$$\log_8\ \frac{1}{2}=64$$

Answer

$$\log_{64}\ \frac{1}{2}=8$$

Question 27

Which of the following is the correct graph for the logarithmic function $$f(x) = \log_2(x-3)$$ ?

Accepted Answer

Graph passing through $$(4,0)$$ with a vertical asymptote at $$x = 3$$

Answer

Graph passing through $$(3,0)$$ with a vertical asymptote at $$x = 0$$

Answer

Graph passing through $$(0,3)$$ with a vertical asymptote at $$x = -3$$

Answer

Graph passing through $$(0,0)$$ with no vertical asymptote

Question 28

Graph the logarithmic function: $$y = \log(x-2)$$

Accepted Answer

The graph is a curve that passes through (3,0) and approaches the line $$x=2$$ asymptotically.

Answer

The graph is a straight line passing through the origin.

Answer

The graph is a parabola opening upwards.

Answer

The graph is a hyperbola.

Question 29

Match the graph with its equation

Accepted Answer

y = log₅ (x + 1) + 1

Answer

y = log₅ (x - 1) + 1

Answer

y = log₅ (x²) + 1

Answer

y = log₅ (x)-1

Question 30

Which graph best represents the following logarithmic function?
$$y=\log_4x$$

Accepted Answer

Option A is correct

Answer

B.

Answer

C.

Answer

D.

Question 31

Write log_b(xy) as two logs

Accepted Answer

log_bx+log_by

Answer

log_bx-log_by

Answer

log_bx*log_by

Answer

log_bx/log_by

Question 32

Graph

Accepted Answer

C

Answer

A

Answer

B

Answer

D

Question 33

Match the graph with its equation

Accepted Answer

y = log₅ (x + 1) + 1

Answer

y = log₅ (x - 1) + 1

Answer

y = log₅ (x²) + 1

Answer

y = log₅ (x)-1

Question 34

Find the corresponding graph of
$$\log_3\left(x\right)-2$$

Accepted Answer

Option A is correct

Answer

B.

Answer

C.

Answer

D.

Logarithmic Functions Graph and Properties

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