Question 1

Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible.
-$\log _ { 4 } ( 6 a b )$

Accepted Answer

A)  $\left( \log _ { 4 } a + \log _ { 4 } b \right) ^ { 6 }$ 
B)  $\log _ { 4 } 6 + \log _ { 4 } ( a + b )$ 
C)  $24 \log _ { 4 } a + 24 \log _ { 4 } b$ 
D)  $\log _ { 4 } 6 + \log _ { 4 } a + \log _ { 4 } b$ 
A)  $\left( \log _ { 4 } a + \log _ { 4 } b \right) ^ { 6 }$ 
B)  $\log _ { 4 } 6 + \log _ { 4 } ( a + b )$ 
C)  $24 \log _ { 4 } a + 24 \log _ { 4 } b$ 
D)  $\log _ { 4 } 6 + \log _ { 4 } a + \log _ { 4 } b$

Question 2

Choose the one alternative that best completes the statement or answers the question.
Solve the equation.
-$$32 ^ { x + 5 } = 4 ^ { 3 x - 1 }$$

Accepted Answer

A)  $\{ 12 \}$ 
B)  $\{ 3 \}$ 
C)  $\{ 27 \}$ 
D)  \{ \} 
A)  $\{ 12 \}$ 
B)  $\{ 3 \}$ 
C)  $\{ 27 \}$ 
D)  \{ \}

Question 3

Write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as
possible.
-$$3 \log _ { 5 } m - 8 \log _ { 5 } n$$

Accepted Answer

A)  $\log _ { 5 } \left( m ^ { 3 } - n ^ { 8 } \right)$ 
B)  $\log _ { 5 } \frac { m ^ { 3 } } { n ^ { 8 } }$ 
C)  $\frac { 3 } { 8 } \log _ { 5 } \frac { m } { n }$ 
D)  $\log _ { 5 } ( 3 m - 8 n )$ 
A)  $\log _ { 5 } \left( m ^ { 3 } - n ^ { 8 } \right)$ 
B)  $\log _ { 5 } \frac { m ^ { 3 } } { n ^ { 8 } }$ 
C)  $\frac { 3 } { 8 } \log _ { 5 } \frac { m } { n }$ 
D)  $\log _ { 5 } ( 3 m - 8 n )$

Question 4

Use the quotient property of logarithms to write the logarithm as a difference of logarithms. Then
simplify if possible.
-$$\log _ { 8 } \frac { t } { 64 }$$

Accepted Answer

A)  $\log _ { 8 } t - \log _ { 8 } 64$ 
B)  $\frac { \log _ { 8 } t } { 2 }$ 
C)  $\log _ { 8 } t - 2$ 
D)  $\frac { \log _ { 8 } t } { \log _ { 8 } 64 }$ 
A)  $\log _ { 8 } t - \log _ { 8 } 64$ 
B)  $\frac { \log _ { 8 } t } { 2 }$ 
C)  $\log _ { 8 } t - 2$ 
D)  $\frac { \log _ { 8 } t } { \log _ { 8 } 64 }$

Question 5

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-The graph of $$f ( x ) = \left( \frac { 3 } { 5 } \right) ^ { x }$$ is (increasing/decreasing) over its domain.

Accepted Answer

The answer of Write the word or phrase that best...

Question 6

The notation ________is often used to represent the inverse of a function f and not the reciprocal of f.

Accepted Answer

The answer of The notation ________is often used to represent...

Question 7

Solve the problem.
-Use the graph of $y = 3 ^ { x }$ to graph the function. Write the domain and range in interval note $f ( x ) = - 3 ^ { x }$

Accepted Answer

A) 
 
Domain: $( - \infty , \infty )$
$\text { Range: }(-\infty, 0)$ 
B) 
 
Domain: $( - \infty , \infty )$
$\text { Range: }(-\infty, 0)$ 
C) 
 
Domain: $( - \infty , \infty )$
Range: $( 0 , \infty )$ 
D) 
 
Domain: $( - \infty , \infty )$
Range: $( 0 , \infty )$ ation. 
A) 
 
Domain: $( - \infty , \infty )$
$\text { Range: }(-\infty, 0)$ 
B) 
 
Domain: $( - \infty , \infty )$
$\text { Range: }(-\infty, 0)$ 
C) 
 
Domain: $( - \infty , \infty )$
Range: $( 0 , \infty )$ 
D) 
 
Domain: $( - \infty , \infty )$
Range: $( 0 , \infty )$ ation.

Question 8

Determine if the given value of x is a solution to the logarithmic equation.
-$$\log _ { 2 } ( x - 63 ) = 6 - \log _ { 2 } x ; x = 64$$

Accepted Answer

A)  No 
B)  Yes 
A)  No 
B)  Yes

Question 9

Choose the one alternative that best completes the statement or answers the question.
Solve the equation.
-$49 ^ { x + 8 } = 7 ^ { 4 x }$

Accepted Answer

A)  $\{ 8 \}$ 
B)  $\left\{ \frac { 10 } { 3 } \right\}$ 
C)  $\left\{ - \frac { 56 } { 3 } \right\}$ 
D)  No solution 
A)  $\{ 8 \}$ 
B)  $\left\{ \frac { 10 } { 3 } \right\}$ 
C)  $\left\{ - \frac { 56 } { 3 } \right\}$ 
D)  No solution

Question 10

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-The function defined by $y = x ^ { 3 }$ (is/is not) an exponential function, whereas the function defined by $y$ $= 3 ^ { x }$ (is/is not) an exponential function.

Accepted Answer

The answer of Write the word or phrase that best...

Question 11

Solve the problem.
-If the half-life of an element is $67 \mathrm { yr }$ and the initial quantity is $3 \mathrm {~kg}$, write a function of the form $Q ( t ) = Q _ { 0 } e ^ { - k t }$ to model the quantity of the element left after $t$ years. Round $k$ to 4 decimal places.

Accepted Answer

A)  $Q ( t ) = 67 e ^ { - 0.0103 t }$ 
B)  $Q ( t ) = 67 e ^ { - 0.0034 t }$ 
C)  $Q ( t ) = 3 e ^ { - 0.0034 t }$ 
D)  $Q ( t ) = 3 e ^ { - 0.0103 t }$ 
A)  $Q ( t ) = 67 e ^ { - 0.0103 t }$ 
B)  $Q ( t ) = 67 e ^ { - 0.0034 t }$ 
C)  $Q ( t ) = 3 e ^ { - 0.0034 t }$ 
D)  $Q ( t ) = 3 e ^ { - 0.0103 t }$

Question 12

Choose the one alternative that best completes the statement or answers the question.
Use the product property of logarithms to write the logarithm as a sum of logarithms. Then simplify if
possible.
-$\log ( c ( c + 4 ) )$

Accepted Answer

A)  $\log c ^ { 2 } + \log 4 c$ 
B)  $2 \log c + \log 4 c$ 
C)  $\log c + \log ( c + 4 )$ 
D)  $3 \log c + \log 4$ 
A)  $\log c ^ { 2 } + \log 4 c$ 
B)  $2 \log c + \log 4 c$ 
C)  $\log c + \log ( c + 4 )$ 
D)  $3 \log c + \log 4$

Question 13

Write the domain in interval notation.
-$$f ( x ) = \ln \left( x ^ { 2 } + 7 \right)$$

Accepted Answer

A)  $( 7 , \infty )$ 
B)  $[ 10 , \infty )$ 
C)  $( - \infty , 7 )$ 
D)  $( - \infty , \infty )$ 
A)  $( 7 , \infty )$ 
B)  $[ 10 , \infty )$ 
C)  $( - \infty , 7 )$ 
D)  $( - \infty , \infty )$

Question 14

Write the domain in interval notation.
-$$f ( x ) = \log _ { 5 } ( 3 - x ) ^ { 2 }$$

Accepted Answer

A)  $( - 3,3 )$ 
B)  $( - \infty , 3 ) \cup ( 3 , \infty )$ 
C)  $( - \infty , \infty )$ 
D)  $( - \infty , - 3 ) \cup ( 3 , \infty )$ 
A)  $( - 3,3 )$ 
B)  $( - \infty , 3 ) \cup ( 3 , \infty )$ 
C)  $( - \infty , \infty )$ 
D)  $( - \infty , - 3 ) \cup ( 3 , \infty )$

Question 15

Given a one-to-one function defined by $y = f ( x )$, if $f ( a ) = f ( b )$, then $a$____$b$

Accepted Answer

The answer of Given a one-to-one function defined by \(y...

Question 16

Approximate $f ( x ) = \ln x$ for the given value of x. Round to four decimal places.
-$f ( \sqrt { 229 } )$

Accepted Answer

A)  1.5133 
B)  2.7169 
C)  2.5133 
D)  1.1799 
A)  1.5133 
B)  2.7169 
C)  2.5133 
D)  1.1799

Question 17

Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible.
-$\log _ { 5 } \frac { a ^ { 8 } } { b ^ { 7 } c }$

Accepted Answer

A)  $8 \log _ { 5 } a + 7 \log _ { 5 } b - \log _ { 5 } c$ 
B)  $8 \log _ { 5 } a - 7 \log _ { 5 } b - \log _ { 5 } c$ 
C)  $8 \log _ { 5 } a - 7 \log _ { 5 } b + \log _ { 5 } c$ 
D)  $8 \log _ { 5 } a + 7 \log _ { 5 } b + \log _ { 5 } c$ 
A)  $8 \log _ { 5 } a + 7 \log _ { 5 } b - \log _ { 5 } c$ 
B)  $8 \log _ { 5 } a - 7 \log _ { 5 } b - \log _ { 5 } c$ 
C)  $8 \log _ { 5 } a - 7 \log _ { 5 } b + \log _ { 5 } c$ 
D)  $8 \log _ { 5 } a + 7 \log _ { 5 } b + \log _ { 5 } c$

Question 18

Solve the equation. Write the solution set with the exact solutions. Also give approximate solutions to 4
decimal places if necessary.
-$\log x - 2 \log 8 = 3$

Accepted Answer

A)  $\{ 768 \}$ 
B)  $\{ 8,000 \}$ 
C)  $\{ 64,000 \}$ 
D)  $\{ 192 \}$ 
A)  $\{ 768 \}$ 
B)  $\{ 8,000 \}$ 
C)  $\{ 64,000 \}$ 
D)  $\{ 192 \}$

Question 19

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-The graph of $f ( x ) = \log _ { 4 } ( x + 6 ) - 8$ is the graph of $y = \log _ { 4 } x$ shifted 6 units (left/right/upward/downward) and shifted 8 units (left/right/upward/downward).

Accepted Answer

The answer of Write the word or phrase that best...

Question 20

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-Given a real number $b$ where $b > 0$ and $b \neq 1$, a function defined by $f ( x ) =$ ــــــــــــ is called an exponential function.

Accepted Answer

The answer of Write the word or phrase that best...

Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible. - $\log _ { 4 } ( 6 a b )$

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $32 ^ { x + 5 } = 4 ^ { 3 x - 1 }$

Write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as possible. - $3 \log _ { 5 } m - 8 \log _ { 5 } n$

Use the quotient property of logarithms to write the logarithm as a difference of logarithms. Then simplify if possible. - $\log _ { 8 } \frac { t } { 64 }$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The graph of $f ( x ) = \left( \frac { 3 } { 5 } \right) ^ { x }$ is (increasing/decreasing) over its domain.

The notation ________is often used to represent the inverse of a function f and not the reciprocal of f.

Solve the problem. -Use the graph of $y = 3 ^ { x }$ to graph the function. Write the domain and range in interval note $f ( x ) = - 3 ^ { x }$

Determine if the given value of x is a solution to the logarithmic equation. - $\log _ { 2 } ( x - 63 ) = 6 - \log _ { 2 } x ; x = 64$

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $49 ^ { x + 8 } = 7 ^ { 4 x }$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The function defined by $y = x ^ { 3 }$ (is/is not) an exponential function, whereas the function defined by $y$ $= 3 ^ { x }$ (is/is not) an exponential function.

Solve the problem. -If the half-life of an element is $67 \mathrm { yr }$ and the initial quantity is $3 \mathrm {~kg}$ , write a function of the form $Q ( t ) = Q _ { 0 } e ^ { - k t }$ to model the quantity of the element left after $t$ years. Round $k$ to 4 decimal places.

Choose the one alternative that best completes the statement or answers the question. Use the product property of logarithms to write the logarithm as a sum of logarithms. Then simplify if possible. - $\log ( c ( c + 4 ) )$

Write the domain in interval notation. - $f ( x ) = \ln \left( x ^ { 2 } + 7 \right)$

Write the domain in interval notation. - $f ( x ) = \log _ { 5 } ( 3 - x ) ^ { 2 }$

Given a one-to-one function defined by $y = f ( x )$ , if $f ( a ) = f ( b )$ , then $a$ ____ $b$

Approximate $f ( x ) = \ln x$ for the given value of x. Round to four decimal places. - $f ( \sqrt { 229 } )$

Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible. - $\log _ { 5 } \frac { a ^ { 8 } } { b ^ { 7 } c }$

Solve the equation. Write the solution set with the exact solutions. Also give approximate solutions to 4 decimal places if necessary. - $\log x - 2 \log 8 = 3$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Given a real number $b$ where $b > 0$ and $b \neq 1$ , a function defined by $f ( x ) =$ ــــــــــــ is called an exponential function.

Equations and Inequalities

Functions and Relations

Polynomial and Rational Functions

Systems of Equations and Inequalities

Matrices and Determinants and Applications

Analytic Geometry

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Exam 4: Exponential and Logarithmic Functions

Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible. - log⁡4(6ab)\log _ { 4 } ( 6 a b )log4​(6ab)

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - 32x+5=43x−132 ^ { x + 5 } = 4 ^ { 3 x - 1 }32x+5=43x−1

Write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as possible. - 3log⁡5m−8log⁡5n3 \log _ { 5 } m - 8 \log _ { 5 } n3log5​m−8log5​n

Use the quotient property of logarithms to write the logarithm as a difference of logarithms. Then simplify if possible. - log⁡8t64\log _ { 8 } \frac { t } { 64 }log8​64t​

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The graph of f(x)=(35)xf ( x ) = \left( \frac { 3 } { 5 } \right) ^ { x }f(x)=(53​)x is (increasing/decreasing) over its domain.

The notation ________is often used to represent the inverse of a function f and not the reciprocal of f.

Solve the problem. -Use the graph of y=3xy = 3 ^ { x }y=3x to graph the function. Write the domain and range in interval note f(x)=−3xf ( x ) = - 3 ^ { x }f(x)=−3x

Determine if the given value of x is a solution to the logarithmic equation. - log⁡2(x−63)=6−log⁡2x;x=64\log _ { 2 } ( x - 63 ) = 6 - \log _ { 2 } x ; x = 64log2​(x−63)=6−log2​x;x=64

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - 49x+8=74x49 ^ { x + 8 } = 7 ^ { 4 x }49x+8=74x

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The function defined by y=x3y = x ^ { 3 }y=x3 (is/is not) an exponential function, whereas the function defined by yyy =3x= 3 ^ { x }=3x (is/is not) an exponential function.

Choose the one alternative that best completes the statement or answers the question. Use the product property of logarithms to write the logarithm as a sum of logarithms. Then simplify if possible. - log⁡(c(c+4))\log ( c ( c + 4 ) )log(c(c+4))

Write the domain in interval notation. - f(x)=ln⁡(x2+7)f ( x ) = \ln \left( x ^ { 2 } + 7 \right)f(x)=ln(x2+7)

Write the domain in interval notation. - f(x)=log⁡5(3−x)2f ( x ) = \log _ { 5 } ( 3 - x ) ^ { 2 }f(x)=log5​(3−x)2

Given a one-to-one function defined by y=f(x)y = f ( x )y=f(x) , if f(a)=f(b)f ( a ) = f ( b )f(a)=f(b) , then aaa ____ bbb

Approximate f(x)=ln⁡xf ( x ) = \ln xf(x)=lnx for the given value of x. Round to four decimal places. - f(229)f ( \sqrt { 229 } )f(229​)

Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible. - log⁡5a8b7c\log _ { 5 } \frac { a ^ { 8 } } { b ^ { 7 } c }log5​b7ca8​

Solve the equation. Write the solution set with the exact solutions. Also give approximate solutions to 4 decimal places if necessary. - log⁡x−2log⁡8=3\log x - 2 \log 8 = 3logx−2log8=3

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Given a real number bbb where b>0b > 0b>0 and b≠1b \neq 1b=1 , a function defined by f(x)=f ( x ) =f(x)= ــــــــــــ is called an exponential function.

Equations and Inequalities

Functions and Relations

Polynomial and Rational Functions

Systems of Equations and Inequalities

Matrices and Determinants and Applications

Analytic Geometry

Sequences, Series, Induction, and Probability

Review of Prerequisites

Filters

Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible. - $\log _ { 4 } ( 6 a b )$

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $32 ^ { x + 5 } = 4 ^ { 3 x - 1 }$

Write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as possible. - $3 \log _ { 5 } m - 8 \log _ { 5 } n$

Use the quotient property of logarithms to write the logarithm as a difference of logarithms. Then simplify if possible. - $\log _ { 8 } \frac { t } { 64 }$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The graph of $f ( x ) = \left( \frac { 3 } { 5 } \right) ^ { x }$ is (increasing/decreasing) over its domain.

Solve the problem. -Use the graph of $y = 3 ^ { x }$ to graph the function. Write the domain and range in interval note $f ( x ) = - 3 ^ { x }$

Determine if the given value of x is a solution to the logarithmic equation. - $\log _ { 2 } ( x - 63 ) = 6 - \log _ { 2 } x ; x = 64$

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $49 ^ { x + 8 } = 7 ^ { 4 x }$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The function defined by $y = x ^ { 3 }$ (is/is not) an exponential function, whereas the function defined by $y$ $= 3 ^ { x }$ (is/is not) an exponential function.

Choose the one alternative that best completes the statement or answers the question. Use the product property of logarithms to write the logarithm as a sum of logarithms. Then simplify if possible. - $\log ( c ( c + 4 ) )$

Write the domain in interval notation. - $f ( x ) = \ln \left( x ^ { 2 } + 7 \right)$

Write the domain in interval notation. - $f ( x ) = \log _ { 5 } ( 3 - x ) ^ { 2 }$

Given a one-to-one function defined by $y = f ( x )$ , if $f ( a ) = f ( b )$ , then $a$ ____ $b$

Approximate $f ( x ) = \ln x$ for the given value of x. Round to four decimal places. - $f ( \sqrt { 229 } )$

Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible. - $\log _ { 5 } \frac { a ^ { 8 } } { b ^ { 7 } c }$

Solve the equation. Write the solution set with the exact solutions. Also give approximate solutions to 4 decimal places if necessary. - $\log x - 2 \log 8 = 3$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Given a real number $b$ where $b > 0$ and $b \neq 1$ , a function defined by $f ( x ) =$ ــــــــــــ is called an exponential function.