Question 1

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

Accepted Answer

A)  $3 ^ { \frac { 1 } { 2 } } = \sqrt { 3 }$ 
B)  $\left( \frac { 1 } { 2 } \right) ^ { 3 } = \sqrt { 3 }$ 
C)  $3 \sqrt{3}=\frac{1}{2}$ 
D)  $\sqrt { 3 } ^ { \frac { 1 } { 2 } } = 3$ 
A)  $3 ^ { \frac { 1 } { 2 } } = \sqrt { 3 }$ 
B)  $\left( \frac { 1 } { 2 } \right) ^ { 3 } = \sqrt { 3 }$ 
C)  $3 \sqrt{3}=\frac{1}{2}$ 
D)  $\sqrt { 3 } ^ { \frac { 1 } { 2 } } = 3$

Question 2

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

Accepted Answer

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

Question 3

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

Accepted Answer

A)  $\frac { \log 2.2 } { 2 \log 6 }$ 
B)  $\frac { 2.2 \log 2 } { \log 6 }$ 
C)  $\frac { \log 2.2 } { 6 \log 2 }$ 
D)  $\frac { 2 \log 2.2 } { \log 6 }$ 
A)  $\frac { \log 2.2 } { 2 \log 6 }$ 
B)  $\frac { 2.2 \log 2 } { \log 6 }$ 
C)  $\frac { \log 2.2 } { 6 \log 2 }$ 
D)  $\frac { 2 \log 2.2 } { \log 6 }$

Question 4

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

Accepted Answer

A)  $f ( x ) = \frac { 1 } { x - 5 } ; g ( x ) = x + 7$ 
B)  $f ( x ) = x + 7 ; g ( x ) = \frac { 5 } { x }$ 
C)  $f ( x ) = \frac { 7 } { x } ; g ( x ) = x - 5$ 
D)  $f ( x ) = \frac { 5 } { x } ; g ( x ) = x + 7$ 
A)  $f ( x ) = \frac { 1 } { x - 5 } ; g ( x ) = x + 7$ 
B)  $f ( x ) = x + 7 ; g ( x ) = \frac { 5 } { x }$ 
C)  $f ( x ) = \frac { 7 } { x } ; g ( x ) = x - 5$ 
D)  $f ( x ) = \frac { 5 } { x } ; g ( x ) = x + 7$

Question 5

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

Accepted Answer

A)  $\frac { 10 ^ { - 8 } } { 3 }$ 
B)  $- \frac { 80 } { 3 }$ 
C)  $- 24$ 
D)  $\frac { 10 ^ { 3 } } { - 8 }$ 
A)  $\frac { 10 ^ { - 8 } } { 3 }$ 
B)  $- \frac { 80 } { 3 }$ 
C)  $- 24$ 
D)  $\frac { 10 ^ { 3 } } { - 8 }$

Question 6

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

Accepted Answer

A)  4 
B)  $\frac { 5 } { 2 }$ 
C)  0 
D)  $\log 2$ 
A)  4 
B)  $\frac { 5 } { 2 }$ 
C)  0 
D)  $\log 2$

Question 7

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

Accepted Answer

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

Question 8

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

Accepted Answer

A)  $f ^ { - 1 } ( x ) = - \frac { x - 9 } { 6 }$ 
B)  $f ^ { - 1 } ( x ) = \frac { x - 9 } { 6 }$ 
C)  $f ^ { - 1 } ( x ) = - \frac { x + 6 } { 9 }$ 
D)  $f ^ { - 1 } ( x ) = \frac { x + 9 } { 6 }$ 
A)  $f ^ { - 1 } ( x ) = - \frac { x - 9 } { 6 }$ 
B)  $f ^ { - 1 } ( x ) = \frac { x - 9 } { 6 }$ 
C)  $f ^ { - 1 } ( x ) = - \frac { x + 6 } { 9 }$ 
D)  $f ^ { - 1 } ( x ) = \frac { x + 9 } { 6 }$

Question 9

Graph the exponential function.
-$y = - \left( \frac { 1 } { 3 } \right) ^ { x }$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 10

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

Accepted Answer

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

Question 11

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

Accepted Answer

A)  $\log _ { y } 7 x$ 
B)  $\log _ { y } 9 + \log _ { y } x - \log _ { y } 2$ 
C)  $\log _ { y } 9 + \log _ { y } x + \log _ { y } 2$ 
D)  $\log _ { y } 9 x - \log _ { y } 2$ 
A)  $\log _ { y } 7 x$ 
B)  $\log _ { y } 9 + \log _ { y } x - \log _ { y } 2$ 
C)  $\log _ { y } 9 + \log _ { y } x + \log _ { y } 2$ 
D)  $\log _ { y } 9 x - \log _ { y } 2$

Question 12

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

Accepted Answer

A)  19 
B)  6 
C)  $\frac { 62 } { 3 }$ 
D)  22 
A)  19 
B)  6 
C)  $\frac { 62 } { 3 }$ 
D)  22

Question 13

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

Accepted Answer

A)  22 
B)  $- 2.2$ 
C)  $2.2$ 
D)  $\log 2.2$ 
A)  22 
B)  $- 2.2$ 
C)  $2.2$ 
D)  $\log 2.2$

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.
-$\mathrm { f } = \{ ( 0,0 ) , ( 1,1 ) , ( - 2,8 ) \}$

Accepted Answer

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

Question 15

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

Accepted Answer

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

Question 16

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

Accepted Answer

A)  $\frac { 1 } { 2 }$ 
B)  $- 7$ 
C)  $\varnothing$ 
D)  7 
A)  $\frac { 1 } { 2 }$ 
B)  $- 7$ 
C)  $\varnothing$ 
D)  7

Question 17

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

Accepted Answer

A)  $0.2718$ 
B)  $0.4$ 
C)  $0.6107$ 
D)  $0.6749$ 
A)  $0.2718$ 
B)  $0.4$ 
C)  $0.6107$ 
D)  $0.6749$

Question 18

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

Accepted Answer

A)  $f ^ { - 1 } ( x ) = - x ^ { 3 } - 8$ 
B)  $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x - 8 }$ 
C)  $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x + 8 }$ 
D)  $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x } - 8$ 
A)  $f ^ { - 1 } ( x ) = - x ^ { 3 } - 8$ 
B)  $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x - 8 }$ 
C)  $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x + 8 }$ 
D)  $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x } - 8$

Question 19

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

Accepted Answer

A)  $\log _ { 6 } \frac { x ^ { 5 } } { x + 9 }$ 
B)  $\log _ { 6 } \left[ x ^ { 5 } ( x + 9 ) \right]$ 
C)  $\log _ { 6 } \frac { x ^ { 3 } } { x + 9 }$ 
D)  $\log _ { 6 } \frac { x + 9 } { x ^ { 3 } }$ 
A)  $\log _ { 6 } \frac { x ^ { 5 } } { x + 9 }$ 
B)  $\log _ { 6 } \left[ x ^ { 5 } ( x + 9 ) \right]$ 
C)  $\log _ { 6 } \frac { x ^ { 3 } } { x + 9 }$ 
D)  $\log _ { 6 } \frac { x + 9 } { x ^ { 3 } }$

Question 20

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

Accepted Answer

A)  $\log _ { 9 } ^3 = 2$ 
B)  $\log _ { 2 } ^9 = 3$ 
C)  $\log _ { 3 } ^9 = 2$ 
D)  $\log _ { 3 } ^2 = 9$ 
A)  $\log _ { 9 } ^3 = 2$ 
B)  $\log _ { 2 } ^9 = 3$ 
C)  $\log _ { 3 } ^9 = 2$ 
D)  $\log _ { 3 } ^2 = 9$

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

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

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

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

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

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

Write the function F(x) as a composition of f, g, or h. - f(x)=-2g(x)=-6xh(x)= F(x)=36-2

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

Graph the exponential function. - $y = - \left( \frac { 1 } { 3 } \right) ^ { x }$ $Graph the exponential function. - y = - \left( \frac { 1 } { 3 } \right) ^ { x }$

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

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

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

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

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. - $\mathrm { f } = \{ ( 0,0 ) , ( 1,1 ) , ( - 2,8 ) \}$

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

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

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

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

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

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

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Solving Systems of Linear Equations

Exponents and Polynomials

Factoring Polynomials

Rational Expressions

More on Functions and Graphs

Inequalities and Absolute Value

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 12: Exponential and Logarithmic Functions

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

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

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

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​

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

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