Question 1

Write the expression as sums or differences of multiples of logarithms.
- log⁡y9x2\log _ { y } \frac { 9 x } { 2 }logy​29x​

Accepted Answer

A)    log⁡y7x\log _ { y } 7 xlogy​7x 
B)    log⁡y9+log⁡yx−log⁡y2\log _ { y } 9 + \log _ { y } x - \log _ { y } 2logy​9+logy​x−logy​2 
C)    log⁡y9+log⁡yx+log⁡y2\log _ { y } 9 + \log _ { y } x + \log _ { y } 2logy​9+logy​x+logy​2 
D)    log⁡y9x−log⁡y2\log _ { y } 9 x - \log _ { y } 2logy​9x−logy​2

Question 2

Solve the equation for x. Give an exact solution.
- log⁡3x=−8\log 3 x = - 8log3x=−8

Accepted Answer

A)    10−83\frac { 10 ^ { - 8 } } { 3 }310−8​ 
B)    −803- \frac { 80 } { 3 }−380​ 
C)    −24- 24−24 
D)    103−8\frac { 10 ^ { 3 } } { - 8 }−8103​

Question 3

Solve the logarithmic equation for x. Give an exact solution
- log⁡8(3x−2) =2\log _ { 8 } ( 3 x - 2 )  = 2log8​(3x−2) =2

Accepted Answer

A)   19
B)   6
C)    623\frac { 62 } { 3 }362​ 
D)   22

Question 4

Solve the equation for x. Give an approximate solution accurate to four decimal places.
- ln⁡2x=0.2\ln 2 x = 0.2ln2x=0.2

Accepted Answer

A)    0.27180.27180.2718 
B)    0.40.40.4 
C)    0.61070.61070.6107 
D)    0.67490.67490.6749

Question 5

Write the function F(x)  as a composition of f, g, or h.
- f(x) =x2−2g(x) =−6xh(x) =x−1F(x) =36x2−2\begin{array} { l } f ( x )  = x ^ { 2 } - 2 \quad g ( x )  = - 6 x \quad h ( x )  = \sqrt { x - 1 } \F ( x )  = 36 x ^ { 2 } - 2\end{array}f(x) =x2−2g(x) =−6xh(x) =x−1​F(x) =36x2−2​

Accepted Answer

A)    F(x) =(g∘f) (x) F ( x )  = ( g \circ f )  ( x ) F(x) =(g∘f) (x)  
B)    F(x) =(g∘h) (x) F ( x )  = ( g \circ h )  ( x ) F(x) =(g∘h) (x)  
C)    F(x) =(f∘g) (x) F ( x )  = ( f \circ g )  ( x ) F(x) =(f∘g) (x)  
D)    F(x) =(h∘g) (x) F ( x )  = ( h \circ g )  ( x ) F(x) =(h∘g) (x)

Question 6

Find the inverse of the one-to-one function.
- f(x) =6x+9f ( x )  = 6 x + 9f(x) =6x+9

Accepted Answer

A)    f−1(x) =−x−96f ^ { - 1 } ( x )  = - \frac { x - 9 } { 6 }f−1(x) =−6x−9​ 
B)    f−1(x) =x−96f ^ { - 1 } ( x )  = \frac { x - 9 } { 6 }f−1(x) =6x−9​ 
C)    f−1(x) =−x+69f ^ { - 1 } ( x )  = - \frac { x + 6 } { 9 }f−1(x) =−9x+6​ 
D)    f−1(x) =x+96f ^ { - 1 } ( x )  = \frac { x + 9 } { 6 }f−1(x) =6x+9​

Question 7

Solve the equation.
- log⁡4(x−5) =4\log _ { 4 } ( x - 5 )  = 4log4​(x−5) =4

Accepted Answer

A)   11
B)   21
C)   261
D)   251

Question 8

Provide an appropriate response.
-Solve  6x−2=1366 ^ { x - 2 } = \frac { 1 } { 36 }6x−2=361​  for  xxx . Give an exact solution.

Accepted Answer

A)   4
B)    52\frac { 5 } { 2 }25​ 
C)   0
D)    log⁡2\log 2log2

Question 9

Find the exact value.
- ln⁡e2.2\ln \mathrm { e } ^ { 2.2 }lne2.2

Accepted Answer

A)   22
B)    −2.2- 2.2−2.2 
C)    2.22.22.2 
D)    log⁡2.2\log 2.2log2.2

Question 10

Approximate the logarithm to four decimal places using the change of base formula.
- log⁡215\log _ { 2 } \frac { 1 } { 5 }log2​51​

Accepted Answer

A)    −0.4307- 0.4307−0.4307 
B)    −1.0000- 1.0000−1.0000 
C)    −0.3979- 0.3979−0.3979 
D)    −2.3219- 2.3219−2.3219

Question 11

Find the inverse of the one-to-one function.
- f(x) =x3+8f ( x )  = x ^ { 3 } + 8f(x) =x3+8

Accepted Answer

A)    f−1(x) =−x3−8f ^ { - 1 } ( x )  = - x ^ { 3 } - 8f−1(x) =−x3−8 
B)    f−1(x) =x−83f ^ { - 1 } ( x )  = \sqrt [ 3 ] { x - 8 }f−1(x) =3x−8c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
C)    f−1(x) =x+83f ^ { - 1 } ( x )  = \sqrt [ 3 ] { x + 8 }f−1(x) =3x+8c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
D)    f−1(x) =x3−8f ^ { - 1 } ( x )  = \sqrt [ 3 ] { x } - 8f−1(x) =3xc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​−8

Question 12

Use the properties of logarithms to write the expression as a single logarithm.
- log⁡6x+4log⁡6x−log⁡6(x+9) \log _ { 6 } x + 4 \log _ { 6 } x - \log _ { 6 } ( x + 9 ) log6​x+4log6​x−log6​(x+9)

Accepted Answer

A)    log⁡6x5x+9\log _ { 6 } \frac { x ^ { 5 } } { x + 9 }log6​x+9x5​ 
B)    log⁡6[x5(x+9) ]\log _ { 6 } \left[ x ^ { 5 } ( x + 9 )  \right]log6​[x5(x+9) ] 
C)    log⁡6x3x+9\log _ { 6 } \frac { x ^ { 3 } } { x + 9 }log6​x+9x3​ 
D)    log⁡6x+9x3\log _ { 6 } \frac { x + 9 } { x ^ { 3 } }log6​x3x+9​

Question 13

Find f(x)  and g(x)  so that the given function h(x)  = (f ° g) (x) .
- h(x) =5x+7h ( x )  = \frac { 5 } { x + 7 }h(x) =x+75​

Accepted Answer

A)    f(x) =1x−5;g(x) =x+7f ( x )  = \frac { 1 } { x - 5 } ; g ( x )  = x + 7f(x) =x−51​;g(x) =x+7 
B)    f(x) =x+7;g(x) =5xf ( x )  = x + 7 ; g ( x )  = \frac { 5 } { x }f(x) =x+7;g(x) =x5​ 
C)    f(x) =7x;g(x) =x−5f ( x )  = \frac { 7 } { x } ; g ( x )  = x - 5f(x) =x7​;g(x) =x−5 
D)    f(x) =5x;g(x) =x+7f ( x )  = \frac { 5 } { x } ; g ( x )  = x + 7f(x) =x5​;g(x) =x+7

Question 14

Determine whether the function is one-to-one. If it is one-to-one find an equation or a set of ordered pairs that defines
the inverse function of the given function.
- f={(0,0) ,(1,1) ,(−2,8) }\mathrm { f } = \{ ( 0,0 )  , ( 1,1 )  , ( - 2,8 )  \}f={(0,0) ,(1,1) ,(−2,8) }

Accepted Answer

A)   one-to-one;  f−1={(0,0) ,(1,1) ,(8,−2) }\mathrm { f } ^ { - 1 } = \{ ( 0,0 )  , ( 1,1 )  , ( 8 , - 2 )  \}f−1={(0,0) ,(1,1) ,(8,−2) } 
B)   not one-to-one
C)   one-to-one;  f−1={(0,0) ,(1,−2) ,(8,1) }\mathrm { f } ^ { - 1 } = \{ ( 0,0 )  , ( 1 , - 2 )  , ( 8,1 )  \}f−1={(0,0) ,(1,−2) ,(8,1) } 
D)   one-to-one;  f−1={(0,0) ,(1,11) ,(−2,18) }\mathrm { f } ^ { - 1 } = \left\{ ( 0,0 )  , \left( 1 , \frac { 1 } { 1 } \right)  , \left( - 2 , \frac { 1 } { 8 } \right)  \right\}f−1={(0,0) ,(1,11​) ,(−2,81​) }

Question 15

Solve the equation. Give an exact solution.
- 62x=2.26 ^ { 2 x } = 2.262x=2.2

Accepted Answer

A)    log⁡2.22log⁡6\frac { \log 2.2 } { 2 \log 6 }2log6log2.2​ 
B)    2.2log⁡2log⁡6\frac { 2.2 \log 2 } { \log 6 }log62.2log2​ 
C)    log⁡2.26log⁡2\frac { \log 2.2 } { 6 \log 2 }6log2log2.2​ 
D)    2log⁡2.2log⁡6\frac { 2 \log 2.2 } { \log 6 }log62log2.2​

Question 16

Write as an exponential equation.
- log⁡33=12\log _ { 3 } \sqrt { 3 } = \frac { 1 } { 2 }log3​3​=21​

Accepted Answer

A)    312=33 ^ { \frac { 1 } { 2 } } = \sqrt { 3 }321​=3c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
B)    (12) 3=3\left( \frac { 1 } { 2 } \right)  ^ { 3 } = \sqrt { 3 }(21​) 3=3c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
C)    33=123 \sqrt{3}=\frac{1}{2}33c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​=21​ 
D)    312=3\sqrt { 3 } ^ { \frac { 1 } { 2 } } = 33c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​21​=3

Question 17

Solve the equation.
- log⁡(5+x) −log⁡(x−3) =log⁡3\log ( 5 + x )  - \log ( x - 3 )  = \log 3log(5+x) −log(x−3) =log3

Accepted Answer

A)    12\frac { 1 } { 2 }21​ 
B)    −7- 7−7 
C)    ∅\varnothing∅ 
D)   7

Question 18

Write as a logarithmic equation.
- 32=93 ^ { 2 } = 932=9

Accepted Answer

A)    log⁡93=2\log _ { 9 } ^3 = 2log93​=2 
B)    log⁡29=3\log _ { 2 } ^9 = 3log29​=3 
C)    log⁡39=2\log _ { 3 } ^9 = 2log39​=2 
D)    log⁡32=9\log _ { 3 } ^2 = 9log32​=9

Question 19

Graph the exponential function.
- y=−(13) xy = - \left( \frac { 1 } { 3 } \right)  ^ { x }y=−(31​) x

Accepted Answer

A)  
B)  
C)  
D)

Question 20

Determine whether the function is a one-to-one function.
- f={(17,−11) ,(−16,−11) ,(18,17) }\mathrm { f } = \{ ( 17 , - 11 )  , ( - 16 , - 11 )  , ( 18,17 )  \}f={(17,−11) ,(−16,−11) ,(18,17) }

Accepted Answer

A)   one-to-one
B)   not one-to-one

Exam 12: Exponential and Logarithmic Functions

Solve the equation. Give an exact solution. - 62x=2.26 ^ { 2 x } = 2.262x=2.2

Correct AnswerverifiedShow Answer

Find f(x) and g(x) so that the given function h(x) = (f ° g) (x) . - h(x) =5x+7h ( x ) = \frac { 5 } { x + 7 }h(x) =x+75​

Correct AnswerverifiedShow Answer

Graph the exponential function. - y=−(13) xy = - \left( \frac { 1 } { 3 } \right) ^ { x }y=−(31​) x

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Use the properties of logarithms to write the expression as a single logarithm. - log⁡6x+4log⁡6x−log⁡6(x+9) \log _ { 6 } x + 4 \log _ { 6 } x - \log _ { 6 } ( x + 9 ) log6​x+4log6​x−log6​(x+9)

Correct AnswerverifiedShow Answer

Provide an appropriate response. -Solve 6x−2=1366 ^ { x - 2 } = \frac { 1 } { 36 }6x−2=361​ for xxx . Give an exact solution.

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Solve the equation. - log⁡4(x−5) =4\log _ { 4 } ( x - 5 ) = 4log4​(x−5) =4

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Determine whether the function is one-to-one. If it is one-to-one find an equation or a set of ordered pairs that defines the inverse function of the given function. - f={(0,0) ,(1,1) ,(−2,8) }\mathrm { f } = \{ ( 0,0 ) , ( 1,1 ) , ( - 2,8 ) \}f={(0,0) ,(1,1) ,(−2,8) }

Correct AnswerverifiedShow Answer

Write as a logarithmic equation. - 32=93 ^ { 2 } = 932=9

Correct AnswerverifiedShow Answer

Write as an exponential equation. - log⁡33=12\log _ { 3 } \sqrt { 3 } = \frac { 1 } { 2 }log3​3​=21​

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Solve the equation. - log⁡(5+x) −log⁡(x−3) =log⁡3\log ( 5 + x ) - \log ( x - 3 ) = \log 3log(5+x) −log(x−3) =log3

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Solve the equation for x. Give an exact solution. - log⁡3x=−8\log 3 x = - 8log3x=−8

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Find the inverse of the one-to-one function. - f(x) =x3+8f ( x ) = x ^ { 3 } + 8f(x) =x3+8

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Write the expression as sums or differences of multiples of logarithms. - log⁡y9x2\log _ { y } \frac { 9 x } { 2 }logy​29x​

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Find the exact value. - ln⁡e2.2\ln \mathrm { e } ^ { 2.2 }lne2.2

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Find the inverse of the one-to-one function. - f(x) =6x+9f ( x ) = 6 x + 9f(x) =6x+9

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Solve the equation for x. Give an approximate solution accurate to four decimal places. - ln⁡2x=0.2\ln 2 x = 0.2ln2x=0.2

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Write the function F(x) as a composition of f, g, or h. - f(x) =x2−2g(x) =−6xh(x) =x−1F(x) =36x2−2\begin{array} { l } f ( x ) = x ^ { 2 } - 2 \quad g ( x ) = - 6 x \quad h ( x ) = \sqrt { x - 1 } \\F ( x ) = 36 x ^ { 2 } - 2\end{array}f(x) =x2−2g(x) =−6xh(x) =x−1​F(x) =36x2−2​

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Approximate the logarithm to four decimal places using the change of base formula. - log⁡215\log _ { 2 } \frac { 1 } { 5 }log2​51​

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Determine whether the function is a one-to-one function. - f={(17,−11) ,(−16,−11) ,(18,17) }\mathrm { f } = \{ ( 17 , - 11 ) , ( - 16 , - 11 ) , ( 18,17 ) \}f={(17,−11) ,(−16,−11) ,(18,17) }

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Solve the logarithmic equation for x. Give an exact solution - log⁡8(3x−2) =2\log _ { 8 } ( 3 x - 2 ) = 2log8​(3x−2) =2

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Solve the equation. Give an exact solution. - $6 ^ { 2 x } = 2.2$

Correct Answer
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Find f(x) and g(x) so that the given function h(x) = (f ° g) (x) . - $h ( x ) = \frac { 5 } { x + 7 }$

Correct Answer
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Graph the exponential function. - $y = - \left( \frac { 1 } { 3 } \right) ^ { x }$ $Graph the exponential function. - y = - \left( \frac { 1 } { 3 } \right) ^ { x } A) B) C) D)$

Correct Answer
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Use the properties of logarithms to write the expression as a single logarithm. - $\log _ { 6 } x + 4 \log _ { 6 } x - \log _ { 6 } ( x + 9 )$

Correct Answer
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Provide an appropriate response. -Solve $6 ^ { x - 2 } = \frac { 1 } { 36 }$ for $x$ . Give an exact solution.

Correct Answer
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Solve the equation. - $\log _ { 4 } ( x - 5 ) = 4$

Correct Answer
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Determine whether the function is one-to-one. If it is one-to-one find an equation or a set of ordered pairs that defines the inverse function of the given function. - $\mathrm { f } = \{ ( 0,0 ) , ( 1,1 ) , ( - 2,8 ) \}$

Correct Answer
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Write as a logarithmic equation. - $3 ^ { 2 } = 9$

Correct Answer
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Write as an exponential equation. - $\log _ { 3 } \sqrt { 3 } = \frac { 1 } { 2 }$

Correct Answer
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Solve the equation. - $\log ( 5 + x ) - \log ( x - 3 ) = \log 3$

Correct Answer
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Solve the equation for x. Give an exact solution. - $\log 3 x = - 8$

Correct Answer
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Find the inverse of the one-to-one function. - $f ( x ) = x ^ { 3 } + 8$

Correct Answer
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Write the expression as sums or differences of multiples of logarithms. - $\log _ { y } \frac { 9 x } { 2 }$

Correct Answer
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Find the exact value. - $\ln \mathrm { e } ^ { 2.2 }$

Correct Answer
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Find the inverse of the one-to-one function. - $f ( x ) = 6 x + 9$

Correct Answer
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Solve the equation for x. Give an approximate solution accurate to four decimal places. - $\ln 2 x = 0.2$

Correct Answer
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Write the function F(x) as a composition of f, g, or h. - $\begin{array} { l } f ( x ) = x ^ { 2 } - 2 \quad g ( x ) = - 6 x \quad h ( x ) = \sqrt { x - 1 } \\F ( x ) = 36 x ^ { 2 } - 2\end{array}$

Correct Answer
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Approximate the logarithm to four decimal places using the change of base formula. - $\log _ { 2 } \frac { 1 } { 5 }$

Correct Answer
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Determine whether the function is a one-to-one function. - $\mathrm { f } = \{ ( 17 , - 11 ) , ( - 16 , - 11 ) , ( 18,17 ) \}$

Correct Answer
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Solve the logarithmic equation for x. Give an exact solution - $\log _ { 8 } ( 3 x - 2 ) = 2$

Correct Answer
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