Question 1

Solve the equation. Give an exact solution.
-$\mathrm { e } ^ { ( \mathrm { x } + 3 ) } = 7$

Accepted Answer

A)  $\mathrm { e } ^ { 21 }$ 
B)  $\ln 7 - 3$ 
C)  $\ln 10$ 
D)  $\mathrm { e } ^ { 7 } + 3$ 
A)  $\mathrm { e } ^ { 21 }$ 
B)  $\ln 7 - 3$ 
C)  $\ln 10$ 
D)  $\mathrm { e } ^ { 7 } + 3$

Question 2

Solve for x.
-$\log _ { 7 } 1 = x$

Accepted Answer

A)  7 
B)  1 
C)  49 
D)  0 
A)  7 
B)  1 
C)  49 
D)  0

Question 3

Solve the equation.
-$\log _ { 5 } x + \log _ { 5 } ( x + 6 ) = 1$

Accepted Answer

A)  $- 1 + \sqrt { 14 }$ 
B)  $- 3 + \sqrt { 14 }$ 
C)  $3 + \sqrt { 14 }$ 
D)  $- 3 - \sqrt { 14 } , - 3 + \sqrt { 14 }$ 
A)  $- 1 + \sqrt { 14 }$ 
B)  $- 3 + \sqrt { 14 }$ 
C)  $3 + \sqrt { 14 }$ 
D)  $- 3 - \sqrt { 14 } , - 3 + \sqrt { 14 }$

Question 4

Write as an exponential equation.
-$\log _ { \mathrm { e } } \mathrm { z } = 4$

Accepted Answer

A)  $4 ^ { \mathrm { e } } = \mathrm { z }$ 
B)  $e ^ { 4 } = z$ 
C)  $\mathrm { e } ^ { \mathrm { Z } } = 4$ 
D)  $\mathrm { z } ^ { 4 } = \mathrm { e }$ 
A)  $4 ^ { \mathrm { e } } = \mathrm { z }$ 
B)  $e ^ { 4 } = z$ 
C)  $\mathrm { e } ^ { \mathrm { Z } } = 4$ 
D)  $\mathrm { z } ^ { 4 } = \mathrm { e }$

Question 5

Provide an appropriate response.
-If $\log _ { 10 } 2 = 0.3010$ and $\log _ { 10 } 3 = 0.4771$, find the value of $\log _ { 10 } \frac { 27 } { 4 }$.

Accepted Answer

A)  $0.8293$ 
B)  $0.2549$ 
C)  $1.8572$ 
D)  $0.0512$ 
A)  $0.8293$ 
B)  $0.2549$ 
C)  $1.8572$ 
D)  $0.0512$

Question 6

If the function is one-to-one, list the inverse function by switching coordinates or inputs and outputs.
-

Accepted Answer

A) 
  
B) 
  
C) 
  
D)  not one-to-one 
A) 
  
B) 
  
C) 
  
D)  not one-to-one

Question 7

Provide an appropriate response.
-Write the expression $\log _ { 5 } \frac { 4 x ^ { 6 } } { y ^ { 7 } }$ as a sum or difference of multiples of logarithms.

Accepted Answer

A)  $\log _ { 5 } 4 + 6 \log _ { 5 } x + 7 \log _ { 5 } y$ 
B)  $\log _ { 5 } 4 - 6 \log _ { 5 } x - 7 \log _ { 5 } y$ 
C)  $\left( \log _ { 5 } 4 \right) \left( 6 \log _ { 5 } x \right) - 7 \log _ { 5 } y$ 
D)  $\log _ { 5 } 4 + 6 \log _ { 5 } x - 7 \log _ { 5 } y$ 
A)  $\log _ { 5 } 4 + 6 \log _ { 5 } x + 7 \log _ { 5 } y$ 
B)  $\log _ { 5 } 4 - 6 \log _ { 5 } x - 7 \log _ { 5 } y$ 
C)  $\left( \log _ { 5 } 4 \right) \left( 6 \log _ { 5 } x \right) - 7 \log _ { 5 } y$ 
D)  $\log _ { 5 } 4 + 6 \log _ { 5 } x - 7 \log _ { 5 } y$

Question 8

For the given functions f and g, find the requested function.
-$f ( x ) = \sqrt [ 3 ] { x } ; g ( x ) = 5 x - 12 \quad$ Find $( f - g ) ( x )$

Accepted Answer

A)  $( f - g ) ( x ) = \sqrt [ 3 ] { x } + 5 x + 12$ 
B)  $( f - g ) ( x ) = \sqrt [ 3 ] { x } - 5 x + 12$ 
C)  $( f - g ) ( x ) = \sqrt [ 3 ] { x } - 5 x - 12$ 
D)  $( f - g ) ( x ) = - \sqrt [ 3 ] { x } - 5 x + 12$ 
A)  $( f - g ) ( x ) = \sqrt [ 3 ] { x } + 5 x + 12$ 
B)  $( f - g ) ( x ) = \sqrt [ 3 ] { x } - 5 x + 12$ 
C)  $( f - g ) ( x ) = \sqrt [ 3 ] { x } - 5 x - 12$ 
D)  $( f - g ) ( x ) = - \sqrt [ 3 ] { x } - 5 x + 12$

Question 9

Solve the equation. Give an approximate solution to four decimal places.
-$5 ^ { x + 7 } = 4$

Accepted Answer

A)  $8.1610$ 
B)  $- 0.9420$ 
C)  $2.0061$ 
D)  $- 6.1386$ 
A)  $8.1610$ 
B)  $- 0.9420$ 
C)  $2.0061$ 
D)  $- 6.1386$

Question 10

Use the formula A $A = P \left( 1 + \frac { r } { n } \right) ^ { n t } \text { to solve. }$
-Find the amount of money in an account after 3 years if $2300 is deposited at 8% annual interest compounded monthly.

Accepted Answer

A)  $2910.23 
B)  $2897.34 
C)  $2916.96 
D)  $2921.55 
A)  $2910.23 
B)  $2897.34 
C)  $2916.96 
D)  $2921.55

Question 11

$\frac { \log _ { 10 } 3 } { \log _ { 10 } 6 } = \frac { 1 } { 2 }$

Accepted Answer

A) True 
 B)False

Question 12

For the given one-to-one function f, find the following.
-$f ( x ) = \sqrt { 4 x - 3 } - 3$
Find $f ( 3 )$ and $f ^ { - 1 } ( 0 )$.

Accepted Answer

A)  $f ( 3 ) = 0 ; f ^ { - 1 } ( 0 ) = 3$ 
B)  $f ( 3 ) = \frac { 9 } { 4 } ; f ^ { - 1 } ( 0 ) = 0$ 
C)  $f ( 3 ) = 9 ; f ^ { - 1 } ( 0 ) = 3$ 
D)  $f ( 3 ) = 3 ; \mathrm { f } ^ { - 1 } ( 0 ) = 0$ 
A)  $f ( 3 ) = 0 ; f ^ { - 1 } ( 0 ) = 3$ 
B)  $f ( 3 ) = \frac { 9 } { 4 } ; f ^ { - 1 } ( 0 ) = 0$ 
C)  $f ( 3 ) = 9 ; f ^ { - 1 } ( 0 ) = 3$ 
D)  $f ( 3 ) = 3 ; \mathrm { f } ^ { - 1 } ( 0 ) = 0$

Question 13

For the given functions f and g, find the composition.
-$f ( x ) = \sqrt { x + 7 } ; g ( x ) = 8 x - 11 \quad$ Find $( f \circ g ) ( x )$

Accepted Answer

A)  $2 \sqrt { 2 x + 1 }$ 
B)  $8 \sqrt { x + 7 } - 11$ 
C)  $8 \sqrt { x - 4 }$ 
D)  $2 \sqrt { 2 x - 1 }$ 
A)  $2 \sqrt { 2 x + 1 }$ 
B)  $8 \sqrt { x + 7 } - 11$ 
C)  $8 \sqrt { x - 4 }$ 
D)  $2 \sqrt { 2 x - 1 }$

Question 14

Graph the function.
-$f(x)=6 \log x$

Accepted Answer

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

Question 15

Determine whether the functions f and g are inverses of each other.
-$f ( x ) = 4 x + 6 ; g ( x ) = \frac { x + 6 } { 4 }$

Accepted Answer

A) True 
 B)False

Question 16

For the given functions f and g, find the requested function.
-$f ( x ) = 7 x - 6 ; g ( x ) = 2 x - 4 \quad$ Find $( f - g ) ( x )$.

Accepted Answer

A)  $( f - g ) ( x ) = - 5 x + 2$ 
B)  $( f - g ) ( x ) = 9 x - 10$ 
C)  $( f - g ) ( x ) = 5 x - 2$ 
D)  $( f - g ) ( x ) = 5 x - 10$ 
A)  $( f - g ) ( x ) = - 5 x + 2$ 
B)  $( f - g ) ( x ) = 9 x - 10$ 
C)  $( f - g ) ( x ) = 5 x - 2$ 
D)  $( f - g ) ( x ) = 5 x - 10$

Question 17

For the given functions f and g, find the composition.
-$f ( x ) = 6 x ^ { 2 } - 2 x ; g ( x ) = - 3 x \quad$ Find $( g \circ f ) ( x )$.

Accepted Answer

A)  $54 x ^ { 2 } - 2 x$ 
B)  $- 18 x ^ { 3 } + 6 x ^ { 2 }$ 
C)  $6 x ^ { 2 } - 4$ 
D)  $- 18 x ^ { 2 } + 6 x$ 
A)  $54 x ^ { 2 } - 2 x$ 
B)  $- 18 x ^ { 3 } + 6 x ^ { 2 }$ 
C)  $6 x ^ { 2 } - 4$ 
D)  $- 18 x ^ { 2 } + 6 x$

Question 18

Determine whether the function is a one-to-one function.
-$f = \{ ( 8 , - 2 ) , ( - 9,10 ) , ( - 6,9 ) \}$

Accepted Answer

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

Question 19

Solve the equation for x. Give an approximate solution accurate to four decimal places.
-$\log ( 11 x + 2 ) = - 0.1$

Accepted Answer

A)  $- 1.2057$ 
B)  $- 13.2627$ 
C)  $- 0.6028$ 
D)  $- 0.1096$ 
A)  $- 1.2057$ 
B)  $- 13.2627$ 
C)  $- 0.6028$ 
D)  $- 0.1096$

Question 20

Graph the exponential function.
-$y=-5^{x}$

Accepted Answer

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

Solve the equation. Give an exact solution. - $\mathrm { e } ^ { ( \mathrm { x } + 3 ) } = 7$

Solve for x. - $\log _ { 7 } 1 = x$

Solve the equation. - $\log _ { 5 } x + \log _ { 5 } ( x + 6 ) = 1$

Write as an exponential equation. - $\log _ { \mathrm { e } } \mathrm { z } = 4$

Provide an appropriate response. -If $\log _ { 10 } 2 = 0.3010$ and $\log _ { 10 } 3 = 0.4771$ , find the value of $\log _ { 10 } \frac { 27 } { 4 }$ .

If the function is one-to-one, list the inverse function by switching coordinates or inputs and outputs. -

Provide an appropriate response. -Write the expression $\log _ { 5 } \frac { 4 x ^ { 6 } } { y ^ { 7 } }$ as a sum or difference of multiples of logarithms.

For the given functions f and g, find the requested function. - $f ( x ) = \sqrt [ 3 ] { x } ; g ( x ) = 5 x - 12 \quad$ Find $( f - g ) ( x )$

Solve the equation. Give an approximate solution to four decimal places. - $5 ^ { x + 7 } = 4$

Use the formula A $A = P \left( 1 + \frac { r } { n } \right) ^ { n t } \text { to solve. }$ -Find the amount of money in an account after 3 years if $2300 is deposited at 8% annual interest compounded monthly.

$\frac { \log _ { 10 } 3 } { \log _ { 10 } 6 } = \frac { 1 } { 2 }$

For the given one-to-one function f, find the following. - $f ( x ) = \sqrt { 4 x - 3 } - 3$ Find $f ( 3 )$ and $f ^ { - 1 } ( 0 )$ .

For the given functions f and g, find the composition. - $f ( x ) = \sqrt { x + 7 } ; g ( x ) = 8 x - 11 \quad$ Find $( f \circ g ) ( x )$

Graph the function. - $f(x)=6 \log x$ $Graph the function. - f(x)=6 \log x$

Determine whether the functions f and g are inverses of each other. - $f ( x ) = 4 x + 6 ; g ( x ) = \frac { x + 6 } { 4 }$

For the given functions f and g, find the requested function. - $f ( x ) = 7 x - 6 ; g ( x ) = 2 x - 4 \quad$ Find $( f - g ) ( x )$ .

For the given functions f and g, find the composition. - $f ( x ) = 6 x ^ { 2 } - 2 x ; g ( x ) = - 3 x \quad$ Find $( g \circ f ) ( x )$ .

Determine whether the function is a one-to-one function. - $f = \{ ( 8 , - 2 ) , ( - 9,10 ) , ( - 6,9 ) \}$

Solve the equation for x. Give an approximate solution accurate to four decimal places. - $\log ( 11 x + 2 ) = - 0.1$

Graph the exponential function. - $y=-5^{x}$ $Graph the exponential function. - y=-5^{x}$

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

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Exam 12: Exponential and Logarithmic Functions

Solve the equation. Give an exact solution. - e(x+3)=7\mathrm { e } ^ { ( \mathrm { x } + 3 ) } = 7e(x+3)=7

Solve for x. - log⁡71=x\log _ { 7 } 1 = xlog7​1=x

Solve the equation. - log⁡5x+log⁡5(x+6)=1\log _ { 5 } x + \log _ { 5 } ( x + 6 ) = 1log5​x+log5​(x+6)=1

Write as an exponential equation. - log⁡ez=4\log _ { \mathrm { e } } \mathrm { z } = 4loge​z=4

Provide an appropriate response. -If log⁡102=0.3010\log _ { 10 } 2 = 0.3010log10​2=0.3010 and log⁡103=0.4771\log _ { 10 } 3 = 0.4771log10​3=0.4771 , find the value of log⁡10274\log _ { 10 } \frac { 27 } { 4 }log10​427​ .

If the function is one-to-one, list the inverse function by switching coordinates or inputs and outputs. -

Provide an appropriate response. -Write the expression log⁡54x6y7\log _ { 5 } \frac { 4 x ^ { 6 } } { y ^ { 7 } }log5​y74x6​ as a sum or difference of multiples of logarithms.

For the given functions f and g, find the requested function. - f(x)=x3;g(x)=5x−12f ( x ) = \sqrt [ 3 ] { x } ; g ( x ) = 5 x - 12 \quadf(x)=3x​;g(x)=5x−12 Find (f−g)(x)( f - g ) ( x )(f−g)(x)

Solve the equation. Give an approximate solution to four decimal places. - 5x+7=45 ^ { x + 7 } = 45x+7=4

Use the formula A A=P(1+rn)nt to solve. A = P \left( 1 + \frac { r } { n } \right) ^ { n t } \text { to solve. }A=P(1+nr​)nt to solve. -Find the amount of money in an account after 3 years if $2300 is deposited at 8% annual interest compounded monthly.

log⁡103log⁡106=12\frac { \log _ { 10 } 3 } { \log _ { 10 } 6 } = \frac { 1 } { 2 }log10​6log10​3​=21​

For the given one-to-one function f, find the following. - f(x)=4x−3−3f ( x ) = \sqrt { 4 x - 3 } - 3f(x)=4x−3​−3 Find f(3)f ( 3 )f(3) and f−1(0)f ^ { - 1 } ( 0 )f−1(0) .

For the given functions f and g, find the composition. - f(x)=x+7;g(x)=8x−11f ( x ) = \sqrt { x + 7 } ; g ( x ) = 8 x - 11 \quadf(x)=x+7​;g(x)=8x−11 Find (f∘g)(x)( f \circ g ) ( x )(f∘g)(x)

Graph the function. - f(x)=6log⁡xf(x)=6 \log xf(x)=6logx

Determine whether the functions f and g are inverses of each other. - f(x)=4x+6;g(x)=x+64f ( x ) = 4 x + 6 ; g ( x ) = \frac { x + 6 } { 4 }f(x)=4x+6;g(x)=4x+6​

For the given functions f and g, find the requested function. - f(x)=7x−6;g(x)=2x−4f ( x ) = 7 x - 6 ; g ( x ) = 2 x - 4 \quadf(x)=7x−6;g(x)=2x−4 Find (f−g)(x)( f - g ) ( x )(f−g)(x) .

For the given functions f and g, find the composition. - f(x)=6x2−2x;g(x)=−3xf ( x ) = 6 x ^ { 2 } - 2 x ; g ( x ) = - 3 x \quadf(x)=6x2−2x;g(x)=−3x Find (g∘f)(x)( g \circ f ) ( x )(g∘f)(x) .

Determine whether the function is a one-to-one function. - f={(8,−2),(−9,10),(−6,9)}f = \{ ( 8 , - 2 ) , ( - 9,10 ) , ( - 6,9 ) \}f={(8,−2),(−9,10),(−6,9)}

Solve the equation for x. Give an approximate solution accurate to four decimal places. - log⁡(11x+2)=−0.1\log ( 11 x + 2 ) = - 0.1log(11x+2)=−0.1

Graph the exponential function. - y=−5xy=-5^{x}y=−5x

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

Solve the equation. Give an exact solution. - $\mathrm { e } ^ { ( \mathrm { x } + 3 ) } = 7$

Solve for x. - $\log _ { 7 } 1 = x$

Solve the equation. - $\log _ { 5 } x + \log _ { 5 } ( x + 6 ) = 1$

Write as an exponential equation. - $\log _ { \mathrm { e } } \mathrm { z } = 4$

Provide an appropriate response. -If $\log _ { 10 } 2 = 0.3010$ and $\log _ { 10 } 3 = 0.4771$ , find the value of $\log _ { 10 } \frac { 27 } { 4 }$ .

Provide an appropriate response. -Write the expression $\log _ { 5 } \frac { 4 x ^ { 6 } } { y ^ { 7 } }$ as a sum or difference of multiples of logarithms.

For the given functions f and g, find the requested function. - $f ( x ) = \sqrt [ 3 ] { x } ; g ( x ) = 5 x - 12 \quad$ Find $( f - g ) ( x )$

Solve the equation. Give an approximate solution to four decimal places. - $5 ^ { x + 7 } = 4$

Use the formula A $A = P \left( 1 + \frac { r } { n } \right) ^ { n t } \text { to solve. }$ -Find the amount of money in an account after 3 years if $2300 is deposited at 8% annual interest compounded monthly.

$\frac { \log _ { 10 } 3 } { \log _ { 10 } 6 } = \frac { 1 } { 2 }$

For the given one-to-one function f, find the following. - $f ( x ) = \sqrt { 4 x - 3 } - 3$ Find $f ( 3 )$ and $f ^ { - 1 } ( 0 )$ .

For the given functions f and g, find the composition. - $f ( x ) = \sqrt { x + 7 } ; g ( x ) = 8 x - 11 \quad$ Find $( f \circ g ) ( x )$

Graph the function. - $f(x)=6 \log x$ $Graph the function. - f(x)=6 \log x$

Determine whether the functions f and g are inverses of each other. - $f ( x ) = 4 x + 6 ; g ( x ) = \frac { x + 6 } { 4 }$

For the given functions f and g, find the requested function. - $f ( x ) = 7 x - 6 ; g ( x ) = 2 x - 4 \quad$ Find $( f - g ) ( x )$ .

For the given functions f and g, find the composition. - $f ( x ) = 6 x ^ { 2 } - 2 x ; g ( x ) = - 3 x \quad$ Find $( g \circ f ) ( x )$ .

Determine whether the function is a one-to-one function. - $f = \{ ( 8 , - 2 ) , ( - 9,10 ) , ( - 6,9 ) \}$

Solve the equation for x. Give an approximate solution accurate to four decimal places. - $\log ( 11 x + 2 ) = - 0.1$

Graph the exponential function. - $y=-5^{x}$ $Graph the exponential function. - y=-5^{x}$