Question 1

Find the graph of the function.​  y=log⁡2xy = \log _ { 2 } xy=log2​x  ​

Accepted Answer

A)   
B)   
C)   
D)    E) A) and D)
F) C) and D)

Question 2

Write the logarithmic equation in exponential form.​  log⁡7149=−2\log _ { 7 } \frac { 1 } { 49 } = - 2log7​491​=−2  ​

Accepted Answer

A)    7−2=−1497 ^ { - 2 } = - \frac { 1 } { 49 }7−2=−491​ 
B)    7−2=1497 ^ { - 2 } = \frac { 1 } { 49 }7−2=491​ 
C)    7−2=−497 ^ { - 2 } = - 497−2=−49 
D)    7−2=497 ^ { - 2 } = 497−2=49 
E)    49−2=1749 ^ { - 2 } = \frac { 1 } { 7 }49−2=71​F) A) and D)
G) A) and E) B

Question 3

Use the One-to-One Property to solve the equation for x.​  log⁡7(x+5) =log⁡715\log _ { 7 } ( x + 5 )  = \log _ { 7 } 15log7​(x+5) =log7​15  ​

Accepted Answer

A)  13
B)  11
C)  12
D)  10
E)  14 F) C) and D)
G) B) and E)

Question 4

Evaluate the function at the indicated value of  x=14x = \frac { 1 } { 4 }x=41​  .Round your result to three decimal places.​  g(x) =−ln⁡xg ( x )  = - \ln xg(x) =−lnx  ​

Accepted Answer

A)  -1.386
B)  4
C)  2.079
D)  -2.079
E)  1.386 F) C) and D)
G) B) and C)

Question 5

Write the logarithmic equation in exponential form.​  ln⁡(295) =5.687…\ln ( 295 )  = 5.687 \ldotsln(295) =5.687…  ​

Accepted Answer

A)    e5.687⋯=−295e ^ { 5.687 \cdots } = - 295e5.687⋯=−295 
B)    e5.687…=295e ^ { 5.687 \ldots } = 295e5.687…=295 
C)    e−5.687⋯=−295e ^ { - 5.687 \cdots } = - 295e−5.687⋯=−295 
D)    e5.687…=1295e ^ { 5.687 \ldots } = \frac { 1 } { 295 }e5.687…=2951​ 
E)    e−5.687⋯=295e ^ { - 5.687 \cdots } = 295e−5.687⋯=295F) A) and C)
G) D) and E)

Question 6

Use the properties of logarithms to simplify the expression.​  9log⁡9179 ^ { \log _ { 9 } 17 }9log9​17  ​

Accepted Answer

A)  17
B)  0
C)    −117- \frac { 1 } { 17 }−171​ 
D)  -17
E)    117\frac { 1 } { 17 }171​F) C) and D)
G) B) and C)

Question 7

Evaluate the function at the indicated value of  x=1x = 1x=1  .​  f(x) =log⁡8xf ( x )  = \log _ { 8 } xf(x) =log8​x  ​

Accepted Answer

A)    18\frac { 1 } { 8 }81​ 
B)    −18- \frac { 1 } { 8 }−81​ 
C)  -8
D)  0
E)  8 F) B) and E)
G) A) and E)

Question 8

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

Accepted Answer

A)  -0.587
B)  0.609
C)  -0.609
D)  0.683
E)  undefined F) A) and B)
G) A) and C)

Question 9

Write the exponential equation  e5/2=12.1825…e ^ { 5 / 2 } = 12.1825 \ldotse5/2=12.1825…  in logarithmic form.

Accepted Answer

A)    2.303log⁡(52) =12.1825…2.303 \log \left( \frac { 5 } { 2 } \right)  = 12.1825 \ldots2.303log(25​) =12.1825… 
B)    log⁡10(12.1825…) =52\log _ { 10 } ( 12.1825 \ldots )  = \frac { 5 } { 2 }log10​(12.1825…) =25​ 
C)    ln⁡(52) =12.1825…\ln \left( \frac { 5 } { 2 } \right)  = 12.1825 \ldotsln(25​) =12.1825… 
D)    ln⁡(12.1825…) =52\ln ( 12.1825 \ldots )  = \frac { 5 } { 2 }ln(12.1825…) =25​ 
E)    ln⁡(5) =12.1825…2\ln ( 5 )  = \frac { 12.1825 \ldots } { 2 }ln(5) =212.1825…​F) A) and B)
G) A) and C) D

Question 10

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

Accepted Answer

A)    x=2x = 2x=2 
B)    x=4x = 4x=4 
C)    x=0x = 0x=0 
D)    x=3x = 3x=3 
E)  The function has no x-intercept. F) All of the above
G) C) and D)

Question 11

Write the logarithmic equation in exponential form.​  log⁡10010=12\log _ { 100 } 10 = \frac { 1 } { 2 }log100​10=21​  ​

Accepted Answer

A)    1001/2=−10100 ^ { 1 / 2 } = - 101001/2=−10 
B)    1001/2=10100 ^ { 1 / 2 } = 101001/2=10 
C)    101/2=10010 ^ { 1 / 2 } = 100101/2=100 
D)    1001/2=−110100 ^ { 1 / 2 } = - \frac { 1 } { 10 }1001/2=−101​ 
E)    1001/2=110100 ^ { 1 / 2 } = \frac { 1 } { 10 }1001/2=101​F) D) and E)
G) None of the above

Question 12

Evaluate the function at the indicated value of  x=64x = 64x=64  .​  f(x) =log⁡8xf ( x )  = \log _ { 8 } xf(x) =log8​x  ​

Accepted Answer

A)  0
B)    −12- \frac { 1 } { 2 }−21​ 
C)    12\frac { 1 } { 2 }21​ 
D)  -2
E)  2 F) B) and C)
G) A) and E)

Question 13

Rewrite the logarithmic equation  log⁡4116=−2\log _ { 4 } \frac { 1 } { 16 } = - 2log4​161​=−2  in exponential form.

Accepted Answer

A)    4−2=−1164 ^ { - 2 } = - \frac { 1 } { 16 }4−2=−161​ 
B)    416=−24 ^ { 16 } = - 2416=−2 
C)    4−2=1164 ^ { - 2 } = \frac { 1 } { 16 }4−2=161​ 
D)    41/16=−24 ^ { 1 / 16 } = - 241/16=−2 
E)    (116) −2=4\left( \frac { 1 } { 16 } \right)  ^ { - 2 } = 4(161​) −2=4F) B) and E)
G) A) and E)

Question 14

Write the exponential equation in logarithmic form.​  2−2=142 ^ { - 2 } = \frac { 1 } { 4 }2−2=41​  ​

Accepted Answer

A)    log⁡412=−2\log _ { 4 } \frac { 1 } { 2 } = - 2log4​21​=−2 
B)    log⁡214=2\log _ { 2 } \frac { 1 } { 4 } = 2log2​41​=2 
C)    log⁡24=2\log _ { 2 } 4 = 2log2​4=2 
D)    log⁡214=−2\log _ { 2 } \frac { 1 } { 4 } = - 2log2​41​=−2 
E)    log⁡24=−2\log _ { 2 } 4 = - 2log2​4=−2F) A) and C)
G) A) and B) D

Question 15

Write the exponential equation in logarithmic form.​  280=128 ^ { 0 } = 1280=1  ​

Accepted Answer

A)    log⁡281=28\log _ { 28 } 1 = 28log28​1=28 
B)    log⁡280=1\log _ { 28 } 0 = 1log28​0=1 
C)    log⁡128=28\log _ { 1 } 28 = 28log1​28=28 
D)    log⁡128=0\log _ { 1 } 28 = 0log1​28=0 
E)    log⁡281=0\log _ { 28 } 1 = 0log28​1=0F) B) and C)
G) C) and D)

Question 16

Write the exponential equation in logarithmic form.​  e3x=4e ^ { 3 x } = 4e3x=4  ​

Accepted Answer

A)    ln⁡4=−3x\ln 4 = - 3 xln4=−3x 
B)    ln⁡4=−13x\ln 4 = - \frac { 1 } { 3 } xln4=−31​x 
C)    ln⁡4=13x\ln 4 = \frac { 1 } { 3 } xln4=31​x 
D)    ln⁡4=3x\ln 4 = 3 xln4=3x 
E)    ln⁡3=4x\ln 3 = 4 xln3=4xF) A) and B)
G) A) and C)

Question 17

Evaluate the function  f(x) =log⁡5xf ( x )  = \log _ { 5 } xf(x) =log5​x  at  x=125x = \frac { 1 } { 25 }x=251​  without using a calculator.

Accepted Answer

A)    125\frac { 1 } { 25 }251​ 
B)  -3
C)  -1
D)  25
E)  -2 F) A) and B)
G) A) and C)

Question 18

Write the logarithmic equation in exponential form.​  ln⁡(8) =2.079…\ln ( 8 )  = 2.079 \ldotsln(8) =2.079…  ​

Accepted Answer

A)    e−2079⋯=−8e ^ { - 2079 \cdots } = - 8e−2079⋯=−8 
B)    e−2079⋯=8e ^ { - 2079 \cdots } = 8e−2079⋯=8 
C)    e2.079⋯=−8e ^ { 2.079 \cdots } = - 8e2.079⋯=−8 
D)    e2.079…=18e ^ { 2.079 \ldots } = \frac { 1 } { 8 }e2.079…=81​ 
E)    e2.079⋯=8e ^ { 2.079 \cdots } = 8e2.079⋯=8F) A) and B)
G) A) and C)

Question 19

Write the exponential equation in logarithmic form.​  811/2=981 ^ { 1 / 2 } = 9811/2=9  ​

Accepted Answer

A)    log⁡819=12\log _ { 81 } 9 = \frac { 1 } { 2 }log81​9=21​ 
B)    log⁡8112=9\log _ { 81 } \frac { 1 } { 2 } = 9log81​21​=9 
C)    log⁡819=2\log _ { 81 } 9 = 2log81​9=2 
D)    log⁡819=−12\log _ { 81 } 9 = - \frac { 1 } { 2 }log81​9=−21​ 
E)    log⁡981=12\log _ { 9 } 81 = \frac { 1 } { 2 }log9​81=21​F) A) and B)
G) A) and C)

Question 20

Write the exponential equation in logarithmic form.​  e1/2=1.649e ^ { 1 / 2 } = 1.649e1/2=1.649  ​

Accepted Answer

A)    ln⁡1.649…=2\ln 1.649 \ldots = 2ln1.649…=2 
B)    ln⁡1.649…=−2\ln 1.649 \ldots = - 2ln1.649…=−2 
C)    ln⁡1.649…=12\ln 1.649 \ldots = \frac { 1 } { 2 }ln1.649…=21​ 
D)    ln⁡2…=1.649\ln 2 \ldots = 1.649ln2…=1.649 
E)    ln⁡1.649…=−12\ln 1.649 \ldots = - \frac { 1 } { 2 }ln1.649…=−21​F) B) and C)
G) A) and C)

Exam 19: Logarithmic Functions and Their Graphs

Find the graph of the function.​ y=log⁡2xy = \log _ { 2 } xy=log2​x ​

Correct AnswerverifiedShow Answer

Write the logarithmic equation in exponential form.​ log⁡7149=−2\log _ { 7 } \frac { 1 } { 49 } = - 2log7​491​=−2 ​

Correct AnswerverifiedB

Use the One-to-One Property to solve the equation for x.​ log⁡7(x+5) =log⁡715\log _ { 7 } ( x + 5 ) = \log _ { 7 } 15log7​(x+5) =log7​15 ​

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Evaluate the function at the indicated value of x=14x = \frac { 1 } { 4 }x=41​ .Round your result to three decimal places.​ g(x) =−ln⁡xg ( x ) = - \ln xg(x) =−lnx ​

Correct AnswerverifiedShow Answer

Write the logarithmic equation in exponential form.​ ln⁡(295) =5.687…\ln ( 295 ) = 5.687 \ldotsln(295) =5.687… ​

Correct AnswerverifiedShow Answer

Use the properties of logarithms to simplify the expression.​ 9log⁡9179 ^ { \log _ { 9 } 17 }9log9​17 ​

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Evaluate the function at the indicated value of x=1x = 1x=1 .​ f(x) =log⁡8xf ( x ) = \log _ { 8 } xf(x) =log8​x ​

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

Correct AnswerverifiedShow Answer

Write the exponential equation e5/2=12.1825…e ^ { 5 / 2 } = 12.1825 \ldotse5/2=12.1825… in logarithmic form.

Correct AnswerverifiedD

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

Correct AnswerverifiedShow Answer

Write the logarithmic equation in exponential form.​ log⁡10010=12\log _ { 100 } 10 = \frac { 1 } { 2 }log100​10=21​ ​

Correct AnswerverifiedShow Answer

Evaluate the function at the indicated value of x=64x = 64x=64 .​ f(x) =log⁡8xf ( x ) = \log _ { 8 } xf(x) =log8​x ​

Correct AnswerverifiedShow Answer

Rewrite the logarithmic equation log⁡4116=−2\log _ { 4 } \frac { 1 } { 16 } = - 2log4​161​=−2 in exponential form.

Correct AnswerverifiedShow Answer

Write the exponential equation in logarithmic form.​ 2−2=142 ^ { - 2 } = \frac { 1 } { 4 }2−2=41​ ​

Correct AnswerverifiedD

Write the exponential equation in logarithmic form.​ 280=128 ^ { 0 } = 1280=1 ​

Correct AnswerverifiedShow Answer

Write the exponential equation in logarithmic form.​ e3x=4e ^ { 3 x } = 4e3x=4 ​

Correct AnswerverifiedShow Answer

Evaluate the function f(x) =log⁡5xf ( x ) = \log _ { 5 } xf(x) =log5​x at x=125x = \frac { 1 } { 25 }x=251​ without using a calculator.

Correct AnswerverifiedShow Answer

Write the logarithmic equation in exponential form.​ ln⁡(8) =2.079…\ln ( 8 ) = 2.079 \ldotsln(8) =2.079… ​

Correct AnswerverifiedShow Answer

Write the exponential equation in logarithmic form.​ 811/2=981 ^ { 1 / 2 } = 9811/2=9 ​

Correct AnswerverifiedShow Answer

Write the exponential equation in logarithmic form.​ e1/2=1.649e ^ { 1 / 2 } = 1.649e1/2=1.649 ​

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

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

Correct Answer
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B

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

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

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

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

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

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

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

Correct Answer
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D

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

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

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

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

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

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D

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

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

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

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

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

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

Correct Answer
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