Deck 19: Logarithmic Functions and Their Graphs

Question 1

Write the exponential equation in logarithmic form.​ $24 ^ { 2 } = 576$ ​

A) $\log _ { 24 } 576 = 2$
B) $\log _ { 24 } 576 = \frac { 1 } { 2 }$
C) $\log _ { 576 } 24 = 2$
D) $\log _ { 24 } 576 = - 2$
E) $\log _ { 24 } 2 = 576$

Answer 1

$\log _ { 24 } 576 = 2$

Question 2

Write the exponential equation in logarithmic form.​ $2 ^ { - 2 } = \frac { 1 } { 4 }$ ​

A) $\log _ { 4 } \frac { 1 } { 2 } = - 2$
B) $\log _ { 2 } \frac { 1 } { 4 } = 2$
C) $\log _ { 2 } 4 = 2$
D) $\log _ { 2 } \frac { 1 } { 4 } = - 2$
E) $\log _ { 2 } 4 = - 2$

Answer 2

$\log _ { 2 } \frac { 1 } { 4 } = - 2$

Question 3

Evaluate the function at the indicated value of $x = 3$ . ​​ $f ( x ) = \log _ { 243 } x$ ​

A) $\frac { 1 } { 5 }$
B)-5
C) $- \frac { 1 } { 5 }$
D)0
E)5

Answer 3

$\frac { 1 } { 5 }$

Question 4

Write the logarithmic equation in exponential form.​ $\log _ { 100 } 10 = \frac { 1 } { 2 }$ ​

A) $100 ^ { 1 / 2 } = - 10$
B) $100 ^ { 1 / 2 } = 10$
C) $10 ^ { 1 / 2 } = 100$
D) $100 ^ { 1 / 2 } = - \frac { 1 } { 10 }$
E) $100 ^ { 1 / 2 } = \frac { 1 } { 10 }$

Question 5

Write the logarithmic equation in exponential form.​ $\log _ { 32 } 2 = \frac { 1 } { 5 }$ ​

A) $32 ^ { 1 / 5 } = - 2$
B) $32 ^ { 1 / 5 } = - \frac { 1 } { 2 }$
C) $2 ^ { 1 / 5 } = 32$
D) $32 ^ { 1 / 5 } = 2$
E) $32 ^ { 1 / 5 } = \frac { 1 } { 2 }$

Question 6

Write the logarithmic equation in exponential form.​ $\log _ { 7 } \frac { 1 } { 49 } = - 2$ ​

A) $7 ^ { - 2 } = - \frac { 1 } { 49 }$
B) $7 ^ { - 2 } = \frac { 1 } { 49 }$
C) $7 ^ { - 2 } = - 49$
D) $7 ^ { - 2 } = 49$
E) $49 ^ { - 2 } = \frac { 1 } { 7 }$

Question 7

Evaluate $f ( x ) = \log x$ at the indicated value of x.Round your result to three decimal places.​ $x = 25.5$ ​

A)-1.407
B)1.407
C)0.711
D)0.039
E)-0.711

Question 8

Write the exponential equation in logarithmic form.​ $28 ^ { 0 } = 1$ ​

A) $\log _ { 28 } 1 = 28$
B) $\log _ { 28 } 0 = 1$
C) $\log _ { 1 } 28 = 28$
D) $\log _ { 1 } 28 = 0$
E) $\log _ { 28 } 1 = 0$

Question 9

Evaluate the function at the indicated value of $x = 64$ .​ $f ( x ) = \log _ { 8 } x$ ​

A)0
B) $- \frac { 1 } { 2 }$
C) $\frac { 1 } { 2 }$
D)-2
E)2

Question 10

Evaluate $f ( x ) = \log x$ at the indicated value of x.Round your result to three decimal places.​ $x = 70.75$ ​

A)1.85
B)0.541
C)0.014
D)-0.541
E)-1.85

Question 11

Write the logarithmic equation in exponential form.​ $\log _ { 15 } \frac { 1 } { 3375 } = - 3$ ​

A) $3375 ^ { - 3 } = \frac { 1 } { 15 }$
B) $15 ^ { - 3 } = - 3375$
C) $15 ^ { - 3 } = 3375$
D) $15 ^ { - 3 } = - \frac { 1 } { 3375 }$
E) $15 ^ { - 3 } = \frac { 1 } { 3375 }$

Question 12

Evaluate $f ( x ) = \log x$ at the indicated value of x.Round your result to three decimal places.​ $x = \frac { 3 } { 2 }$ ​

A)5.682
B)1.5
C)-0.176
D)-5.682
E)0.176

Question 13

Evaluate the function at the indicated value of $x = 281 ^ { 5 }$ .​ $g ( x ) = \log _ { 281 } x$ ​

A)-5
B) $\frac { 1 } { 5 }$
C) $$- \frac { 1 } { 5 }$$
D)5
E)0

Question 14

Write the logarithmic equation in exponential form.​ $\log _ { 7 } 343 = 3$ ​

A) $7 ^ { 343 } = 2$
B) $7 ^ { 3 } = 77$
C) $7 ^ { 3 } = 343$
D) $7 ^ { 3 } = 14$
E) $343 ^ { 7 } = 2$

Question 15

Write the exponential equation in logarithmic form.​ $10 ^ { - 3 } = 0.00100$ ​

A) $\log 3 = 0.00100$
B) $\log 0.00100 = - \frac { 1 } { 3 }$
C) $\log 0.00100 = - 3$
D) $\log 0.00100 = \frac { 1 } { 3 }$
E) $\log 0.00100 = 3$

Question 16

Write the exponential equation in logarithmic form.​ $81 ^ { 1 / 2 } = 9$ ​

A) $\log _ { 81 } 9 = \frac { 1 } { 2 }$
B) $\log _ { 81 } \frac { 1 } { 2 } = 9$
C) $\log _ { 81 } 9 = 2$
D) $\log _ { 81 } 9 = - \frac { 1 } { 2 }$
E) $\log _ { 9 } 81 = \frac { 1 } { 2 }$

Question 17

Write the exponential equation in logarithmic form.​ $2 ^ { 3 } = 8$ ​

A) $\log _ { 8 } 2 = 3$
B) $\log _ { 2 } 8 = 3$
C) $\log _ { 8 } 2 = - 3$
D) $\log _ { 2 } 3 = 8$
E) $\log _ { 2 } 8 = \frac { 1 } { 3 }$

Question 18

Evaluate $f ( x ) = \log x$ at the indicated value of x.Round your result to three decimal places.​ $x = \frac { 1 } { 100 }$ ​

A)-0.5
B)0.01
C)0.5
D)-2
E)2

Question 19

Write the logarithmic equation in exponential form.​ $$\log _ { 5 } 25 = 2$$ ​

A) $25 ^ { 5 } = 2$
B) $5 ^ { 2 } = 10$
C) $5 ^ { 2 } = 55$
D) $5 ^ { 2 } = 25$
E) $5 ^ { 25 } = 2$

Question 20

Evaluate the function at the indicated value of $x = 1$ .​ $f ( x ) = \log _ { 8 } x$ ​

A) $\frac { 1 } { 8 }$
B) $- \frac { 1 } { 8 }$
C)-8
D)0
E)8

Question 21

Write the logarithmic equation in exponential form.​ $\ln \left( \frac { 1 } { 7 } \right) = - 1.946 \ldots$ ​

A) $e ^ { 1.946 ... } = - \frac { 1 } { 7 }$
B) $e ^ { 1.946 \ldots } = \frac { 1 } { 7 }$
C) $e ^ { - 1.946 \ldots } = 7$
D) $e ^ { - 1.946 \ldots } = \frac { 1 } { 7 }$
E) $e ^ { - 1.946 \ldots } = - \frac { 1 } { 7 }$

Question 22

Write the exponential equation in logarithmic form.​ $e ^ { 5 } = 148.413 \ldots$ ​

A) $\ln 148.413 \ldots = - 5$
B) $\ln 148.413 \ldots = - \frac { 1 } { 5 }$
C) $\ln 148.413 \ldots = 5$
D) $\ln 148.413 \ldots = \frac { 1 } { 5 }$
E) $\ln 5 = 148.413 \ldots$

Question 23

Evaluate $g ( x ) = \ln x$ at the indicated value of x.​ $x = e ^ { - 9 }$ ​

A)9
B) $- \frac { 1 } { 9 }$
C)-9
D) $\frac { 1 } { 9 }$
E) $e ^ { - 9 }$

Question 24

Select the graph of the function.​ $$f ( x ) = \ln ( x + 9 )$$ ​

A)​
B)​ ​
C)​
D)​
E)​

Question 25

Evaluate the function at the indicated value of $x = 23.92$ .Round your result to three decimal places.​ $f ( x ) = \ln x$ ​

A)3.175
B)-2.076
C)-3.175
D)2.076
E)23.92

Question 26

Write the exponential equation in logarithmic form.​ $e ^ { - 0.4 } = 0.670 \ldots$ ​

A) $\ln 0.4 = 0.670$
B) $\ln 0.670 \ldots = 0.4$
C) $\ln 0.670 \ldots = \frac { 1 } { 0.4 }$
D) $\ln 0.670 \ldots = - \frac { 1 } { 0.4 }$
E) $\ln 0.670 \ldots = - 0.4$

Question 27

Use the properties of logarithms to simplify the expression.​ $9 ^ { \log _ { 9 } 17 }$ ​

A)17
B)0
C) $- \frac { 1 } { 17 }$
D)-17
E) $\frac { 1 } { 17 }$

Question 28

Evaluate the function at the indicated value of $x = b ^ { - 7 }$ .​ $g ( x ) = \log _ { b } x$ ​

A)7
B)0
C) $\frac { 1 } { 7 }$
D)-7
E) $- \frac { 1 } { 7 }$

Question 29

Use the One-to-One Property to solve the equation for x.​ $$\log _ { 6 } ( 8 x + 8 ) = \log _ { 6 } 4$$ ​

A) $\frac { 3 } { 2 }$
B)-2
C) $- \frac { 1 } { 2 }$
D) $\frac { 1 } { 4 }$
E) $\frac { 2 } { 3 }$

Question 30

Select the graph of the function.​ $$f ( x ) = \log ( x + 5 )$$ ​

A)​
B)​
C)​
D)​
E)​

Question 31

Write the logarithmic equation in exponential form.​ $\ln ( 8 ) = 2.079 \ldots$ ​

A) $e ^ { - 2079 \cdots } = - 8$
B) $e ^ { - 2079 \cdots } = 8$
C) $e ^ { 2.079 \cdots } = - 8$
D) $e ^ { 2.079 \ldots } = \frac { 1 } { 8 }$
E) $e ^ { 2.079 \cdots } = 8$

Question 32

Evaluate $g ( x ) = \ln x$ at the indicated value of x.​ $x = e ^ { 7 }$ ​

A) $- \frac { 1 } { 7 }$
B) $e ^ { 2 }$
C)-7
D)7
E) $\frac { 1 } { 7 }$

Question 33

Write the exponential equation in logarithmic form.​ $e ^ { 3 x } = 4$ ​

A) $\ln 4 = - 3 x$
B) $\ln 4 = - \frac { 1 } { 3 } x$
C) $\ln 4 = \frac { 1 } { 3 } x$
D) $\ln 4 = 3 x$
E) $\ln 3 = 4 x$

Question 34

Write the exponential equation in logarithmic form.​ $e ^ { 1 / 2 } = 1.649$ ​

A) $\ln 1.649 \ldots = 2$
B) $\ln 1.649 \ldots = - 2$
C) $\ln 1.649 \ldots = \frac { 1 } { 2 }$
D) $\ln 2 \ldots = 1.649$
E) $\ln 1.649 \ldots = - \frac { 1 } { 2 }$

Question 35

Evaluate the function at the indicated value of $x = \frac { 1 } { 4 }$ .Round your result to three decimal places.​ $g ( x ) = - \ln x$ ​

A)-1.386
B)4
C)2.079
D)-2.079
E)1.386

Question 36

Use the One-to-One Property to solve the equation for x.​ $$\log _ { 3 } ( x - 4 ) = \log _ { 3 } 6$$ ​

A)11
B)14
C)12
D)13
E)10

Question 37

Evaluate the function at the indicated value of $x = 0.82$ .Round your result to three decimal places.​ $f ( x ) = 9 \ln x$ ​

A)1.786
B)-11.674
C)0.82
D)-1.786
E)11.674

Question 38

Write the logarithmic equation in exponential form.​ $\ln ( 295 ) = 5.687 \ldots$ ​

A) $e ^ { 5.687 \cdots } = - 295$
B) $e ^ { 5.687 \ldots } = 295$
C) $e ^ { - 5.687 \cdots } = - 295$
D) $e ^ { 5.687 \ldots } = \frac { 1 } { 295 }$
E) $e ^ { - 5.687 \cdots } = 295$

Question 39

Use the properties of logarithms to simplify the expression.​ $\log _ { 5 } 5 ^ { 5 }$ ​

A)0
B)​ $- \frac { 1 } { 5 }$
C) $\frac { 1 } { 5 }$
D)-5
E)5

Question 40

Use the One-to-One Property to solve the equation for x.​ $$\log _ { 7 } ( x + 5 ) = \log _ { 7 } 15$$ ​

A)13
B)11
C)12
D)10
E)14

Question 41

Find the graph of the function.​ $$y = \log _ { 5 } ( x - 1 )$$ ​

A)
B)
C)
D)

Question 42

Rewrite the exponential equation $5 ^ { - 3 } = \frac { 1 } { 125 }$ in logarithmic form.

A) $\log _ { 5 } 125 = - 3$
B) $\log _ { 125 } 5 = - 3$
C) $\log _ { 3 } 125 = - 3$
D) $\log _ { 5 } \frac { 1 } { 125 } = - 3$
E) $\log _ { 5 } \frac { 1 } { 125 } = 3$

Question 43

Solve the equation $\log ( 1 - x ) = \log ( 100 )$ for x using the One-to-One Property.

A)-101
B)-1
C)The equation has no solution.
D)-99
E)101

Question 44

Find the value of x.​ $\log _ { 5 } 625 = x$ ​

A)x = 625
B)x = 313
C)x = 5
D)x = 4

Question 45

Use a calculator to find the value for $\log 0.85759$ to four decimal places. ​

A)-0.0667
B)-0.1536
C)0.9333
D)-0.9333
E)0.0667

Question 46

Evaluate the function $f ( x ) = \log _ { 2 } x$ at $x = \frac { 1 } { 2 }$ without using a calculator.

A)0
B)-1
C)-2
D)2
E) $$\frac { 1 } { 2 }$$

Question 47

Write the exponential equation $e ^ { 5 / 2 } = 12.1825 \ldots$ in logarithmic form.

A) $2.303 \log \left( \frac { 5 } { 2 } \right) = 12.1825 \ldots$
B) $\log _ { 10 } ( 12.1825 \ldots ) = \frac { 5 } { 2 }$
C) $\ln \left( \frac { 5 } { 2 } \right) = 12.1825 \ldots$
D) $\ln ( 12.1825 \ldots ) = \frac { 5 } { 2 }$
E) $\ln ( 5 ) = \frac { 12.1825 \ldots } { 2 }$

Question 48

Evaluate the function $f ( x ) = - 3.752 \ln x$ at $x = 4$ .Round to 3 decimal places.(You may use your calculator. )

A)-5.201
B)5.201
C)undefined
D)-2.709
E)0.369

Question 49

Rewrite the logarithmic equation $$\log _ { 4 } \frac { 1 } { 16 } = - 2$$ in exponential form.

A) $4 ^ { 16 } = - 2$
B) $4 ^ { 1 / 16 } = - 2$
C) $4 ^ { - 2 } = \frac { 1 } { 16 }$
D) $\left( \frac { 1 } { 16 } \right) ^ { - 2 } = 4$
E) $4 ^ { - 2 } = - \frac { 1 } { 16 }$

Question 50

Rewrite the logarithmic equation $$\log _ { 4 } \frac { 1 } { 16 } = - 2$$ in exponential form.

A) $4 ^ { - 2 } = - \frac { 1 } { 16 }$
B) $4 ^ { 16 } = - 2$
C) $$4 ^ { - 2 } = \frac { 1 } { 16 }$$
D) $$4 ^ { 1 / 16 } = - 2$$
E) $\left( \frac { 1 } { 16 } \right) ^ { - 2 } = 4$

Question 51

Write the logarithmic equation $\ln 5 = 1.609 \ldots$ in exponential form.

A) $e ^ { 1.609 \cdots } = 5$
B) $10 ^ { 5 } = 1.609 \ldots$
C) $2.303 ^ { 1.609 \ldots } = 5$
D) $2.303 \times 10 ^ { 5 } = 1.609 \ldots$
E) $e ^ { 5 } = 1.609 \ldots$

Question 52

Find the value of b,if any,that would cause the graph of $y = \log _ { b } x$ to look like the graph shown.​ ​

A)b = 3.5
B)b = 4.5
C)b = 2
D)b = 4
E)b = 1

Question 53

Identify the value of the function $f ( x ) = \log _ { 10 } x$ at $x = 915$ .Round to 3 decimal places.

A)6.819
B)3.961
C)2.961
D)4.461
E)3.461

Question 54

Write the exponential equation $e ^ { 3 / 2 } = 4.4817 \ldots$ in logarithmic form.

A) $\ln ( 4.4817 \ldots ) = \frac { 3 } { 2 }$
B) $2.303 \log \left( \frac { 3 } { 2 } \right) = 4.4817 \ldots$
C) $\ln ( 4.4817 \ldots ) = \frac { 2 } { 3 }$
D) $\ln \left( \frac { 3 } { 2 } \right) = 4.4817 \ldots$
E) $\log _ { 10 } ( 4.4817 \ldots ) = \frac { 3 } { 2 }$

Question 55

Identify the x-intercept of the function $f ( x ) = 4 \ln ( x - 2 )$ .

A) $x = 2$
B) $x = 4$
C) $x = 0$
D) $x = 3$
E)The function has no x-intercept.

Question 56

Write the logarithmic equation $\ln 4 = 1.386 \ldots$ in exponential form.

A) $e ^ { 1.386 \cdots } = 4$
B) $e ^ { 4 } = 1.386 \ldots$
C) $2.303 e ^ { 1.386 \cdots } = 4$
D) $10 ^ { 4 } = 1.386 \ldots$
E) $2.303 \times 10 ^ { 4 } = 1.386 \ldots$

Question 57

Identify the value of the function $f ( x ) = \log _ { 10 } x$ at $x = 315$ .Round to 3 decimal places.

A)2.498
B)2.998
C)3.498
D)3.998
E)5.753

Question 58

Evaluate the function $f ( x ) = \log _ { 5 } x$ at $x = \frac { 1 } { 25 }$ without using a calculator.

A) $\frac { 1 } { 25 }$
B)-3
C)-1
D)25
E)-2

Question 59

Write the equation $6 ^ { 5 } = 7,776$ in logarithmic form. ​

A) $\log _ { 6 } 7,776 = 5$
B) $\log _ { 5 } 6 = 7,776$
C) $\log _ { 7,776 } 6 = 5$
D) $\log _ { 6 } 5 = 7,776$
E) $\log _ { 5 } 7,776 = 6$

Question 60

Rewrite the exponential equation $4 ^ { - 2 } = \frac { 1 } { 16 }$ in logarithmic form.

A) $\log _ { 4 } \frac { 1 } { 16 } = - 2$
B) $\log _ { 2 } 16 = - 2$
C) $\log _ { 4 } 16 = - 2$
D) $\log _ { 16 } 4 = - 2$
E) $$\log _ { 4 } \frac { 1 } { 16 } = 2$$

Question 61

Use a calculator to find a value for $\ln ( 30.9 )$ to four decimal places. ​

A)-3.4308
B)3.4308
C)-1.49
D)1.49
E)5.7333

Question 62

Identify the x-intercept of the function $f ( x ) = 4 \ln ( x - 1 )$ .

A) $x = 1$
B) $x = 0$
C) $x = 4$
D) $x = 2$
E)The function has no x-intercept.

Question 63

Find the graph of the function.​ $$y = \log _ { 2 } x$$ ​

A)
B)
C)
D)

Question 64

Evaluate the function $f ( x ) = - 0.944 \ln x$ at $x = 1.906$ .Round to 3 decimal places.(You may use your calculator. )

A)-0.587
B)0.609
C)-0.609
D)0.683
E)undefined