Question 1

Evaluate without the use of a calculator. $\log _ { 4 } 4$

Accepted Answer

1

Question 2

Expand into a sum and/or difference of logarithms. Assume all variables represent positive real numbers. $\log _ { 7 } x ^ { y }$

Accepted Answer

A)  $\log _ { 7 y } x$ 
B)  $\log _ { 7 } x ^ { \log _ { 7 } y }$ 
C)  $\left( \log _ { 7 } x \right) ^ { y }$ 
D)  $y \log _ { 7 } x$ 
A)  $\log _ { 7 y } x$ 
B)  $\log _ { 7 } x ^ { \log _ { 7 } y }$ 
C)  $\left( \log _ { 7 } x \right) ^ { y }$ 
D)  $y \log _ { 7 } x$ D

Question 3

Write the expression as a single logarithm. Assume all variables represent positive real numbers. $$\frac { 1 } { 3 } \ln a - 6 \ln b - \frac { 14 } { 3 } \ln c$$

Accepted Answer

$$\ln \left( \frac { \sqrt [ 3 ] { a } } { b ^ { 6 } c ^ { 4 } \sqrt [ 3 ] { c ^ { 2 } } } \right)$$

Question 4

Find the value of $\log _ { b } 12$, given that $\log _ { b } 3 = 1.025$ and $\log _ { b } 4 = 1.294$.

Accepted Answer

A)  $2.319$ 
B)  $0.269$ 
C)  $1.032$ 
D)  $1.326$ 
A)  $2.319$ 
B)  $0.269$ 
C)  $1.032$ 
D)  $1.326$

Question 5

Which is a logarithmic function?

Accepted Answer

A)  $h ( x ) = \sqrt { 20 x + 12 }$ 
B)  $g ( x ) = \log _ { 20 } x$ 
C)  $f ( x ) = 20 ^ { x + 2 }$ 
D)  $k ( x ) = \frac { 5 x } { x - 20 }$ 
A)  $h ( x ) = \sqrt { 20 x + 12 }$ 
B)  $g ( x ) = \log _ { 20 } x$ 
C)  $f ( x ) = 20 ^ { x + 2 }$ 
D)  $k ( x ) = \frac { 5 x } { x - 20 }$

Question 6

If $m ( x ) = x + 4$ and $n ( x ) = \frac { 1 } { x + 9 }$ find the function value, if possible.
$( n \circ m ) ( - 9 )$

Accepted Answer

A)  $- 5$ 
B)  $\frac { 1 } { 4 }$ 
C)  0 
D)  Undefined 
A)  $- 5$ 
B)  $\frac { 1 } { 4 }$ 
C)  0 
D)  Undefined

Question 7

Solve the logarithmic equation. $$\log _ { 6 } t ^ { 4 } = \log _ { 6 } t ^ { 3 } - 2$$

Accepted Answer

A)  $\{ 36 \}$ 
B)  {  } 
C)  $\left\{ \frac { 1 } { 36 } \right\}$ 
D)  $\{ \sqrt [ 4 ] { 2 } \}$ 
A)  $\{ 36 \}$ 
B)  {  } 
C)  $\left\{ \frac { 1 } { 36 } \right\}$ 
D)  $\{ \sqrt [ 4 ] { 2 } \}$

Question 8

The volume of a can that is 12 centimeters (cm) tall is approximated by the function v $( r ) = 37.68 r ^ { 2 }$ , where r is the radius of the can in cm. Chicken soup costs $0.01 per milliliter (mL) and since $1 \mathrm {~mL} = 1 \mathrm {~cm} ^ { 3 }$ , we can say that chicken soup costs $0.01 \text { per } \mathrm { cm } ^ { 3 }$ . The cost to fill a 12 cm tall can with chicken soup is given by C(v) = 0.01v, where v is the volume of the can in $\mathrm { cm } ^ { 3 }$ .
a. Find $( C \circ v ) ( r )$ and interpret its meaning in the context of this problem.
b. Approximate to the nearest cent the cost to fill a 12 cm can with chicken soup if the can's radius is 5 cm.

Accepted Answer

a. @#LAT-DLM& . This function represents

Question 9

Given that $f ( x ) = 2 x ^ { 2 } + 5$ and $g ( x ) = 4 x + 9$
a. find $( f \circ g ) ( x )$
b. find $( g \circ f ) ( x )$

Accepted Answer

The answer of Given that \(f ( x ) =...

Question 10

Write an equation of the inverse for the one-to-one function as defined. $$z ( x ) = \frac { 1 } { 5 } x - 2$$

Accepted Answer

A)  $z ^ { - 1 } ( x ) = x - 10$ 
B)  $z ^ { - 1 } ( x ) = 5 ( x + 2 )$ 
C)  $z ^ { - 1 } ( x ) = 5 x + 2$ 
D)  $z ^ { - 1 } ( x ) = 5 x - \frac { 1 } { 2 }$ 
A)  $z ^ { - 1 } ( x ) = x - 10$ 
B)  $z ^ { - 1 } ( x ) = 5 ( x + 2 )$ 
C)  $z ^ { - 1 } ( x ) = 5 x + 2$ 
D)  $z ^ { - 1 } ( x ) = 5 x - \frac { 1 } { 2 }$

Question 11

Expand into sums and/or differences of logarithms. Assume all variables represent positive real numbers. $\log \left( \frac { \sqrt [ 3 ] { a b } } { c ^ { 2 } } \right)$

Accepted Answer

A)  $\frac { 1 } { 3 } \log a + \log b - 2 \log c$ 
B)  $3 \log a + \log b - 2 \log c$ 
C)  $\frac { 1 } { 3 } \log a + \frac { 1 } { 3 } \log b - 2 \log c$ 
D)  $\sqrt [ 3 ] { \log a + \log b } + 2 \log c$ 
A)  $\frac { 1 } { 3 } \log a + \log b - 2 \log c$ 
B)  $3 \log a + \log b - 2 \log c$ 
C)  $\frac { 1 } { 3 } \log a + \frac { 1 } { 3 } \log b - 2 \log c$ 
D)  $\sqrt [ 3 ] { \log a + \log b } + 2 \log c$

Question 12

Simplify the expression. Assume all variables represent positive real numbers. $7 e ^ { \ln ( 1 - y ) }$

Accepted Answer

A)  $7 ^ { 1 - y }$ 
B)  $7 - 7 y$ 
C)  $1 - y$ 
D)  $\ln ( 7 - 7 y ) \cdot e$ 
A)  $7 ^ { 1 - y }$ 
B)  $7 - 7 y$ 
C)  $1 - y$ 
D)  $\ln ( 7 - 7 y ) \cdot e$

Question 13

Solve the equation. $$4 ^ { y } = 64$$

Accepted Answer

The answer of Solve the equation. \[4 ^ { y...

Question 14

Solve the logarithmic equation. $$\log _ { 4 } ( c + 7 ) = 3$$

Accepted Answer

A)  $\{ 88 \}$ 
B)  $\{ 74 \}$ 
C)  $\{ 57 \}$ 
D)  $\{ 71 \}$ 
A)  $\{ 88 \}$ 
B)  $\{ 74 \}$ 
C)  $\{ 57 \}$ 
D)  $\{ 71 \}$

Question 15

Write the expression as a single logarithm. Assume all variables represent positive real numbers. $$\frac { 1 } { 3 } \left[ \log \left( a ^ { 2 } + 2 a \right) - \log ( a + 2 ) \right]$$

Accepted Answer

A)  $\log \sqrt [ 3 ] { a }$ 
B)  $\log \sqrt [ 3 ] { a ^ { 2 } + a - 2 }$ 
C)  $\log _ { 1 / 3 } \left( a ^ { 2 } + a - 2 \right)$ 
D)  $\log \left( a ^ { 3 } + 4 a ^ { 2 } + 4 a \right) ^ { 1 / 3 }$ 
A)  $\log \sqrt [ 3 ] { a }$ 
B)  $\log \sqrt [ 3 ] { a ^ { 2 } + a - 2 }$ 
C)  $\log _ { 1 / 3 } \left( a ^ { 2 } + a - 2 \right)$ 
D)  $\log \left( a ^ { 3 } + 4 a ^ { 2 } + 4 a \right) ^ { 1 / 3 }$

Question 16

Solve the exponential equation by taking the logarithm of both sides. $15 e ^ { 0.03 m } = 75$

Accepted Answer

A)  $\left\{ \frac { \ln 0.45 } { 75 } \right\}$ 
B)  $\left\{ \frac { \ln 0.03 } { 5 } \right\}$ 
C)  $\left\{ \frac { \ln 5 } { 0.03 } \right\}$ 
D)  $\left\{ \frac { \ln 75 } { 0.45 } \right\}$ 
A)  $\left\{ \frac { \ln 0.45 } { 75 } \right\}$ 
B)  $\left\{ \frac { \ln 0.03 } { 5 } \right\}$ 
C)  $\left\{ \frac { \ln 5 } { 0.03 } \right\}$ 
D)  $\left\{ \frac { \ln 75 } { 0.45 } \right\}$

Question 17

Graph the function $f ( x ) = 3 ^ { x }$ . Plot at least three points.

Accepted Answer

The answer of Graph the function \(f ( x )...

Question 18

Approximate the function value from the graph. $(f-g)(0)$

Accepted Answer

A)  2 
B)  1 
C)  0 
D)  -1 
A)  2 
B)  1 
C)  0 
D)  -1

Question 19

Graph the equation by completing the table and plotting points. Round to two decimal places when necessary. $f(x)=3 e^{x}$
$\begin{array}{c|c}
x & y \
\hline-2 & \
\hline 0 & \
\hline 1 &
\end{array}$

Accepted Answer

\[\begin{array} { r | l } 
x &

Question 20

Graph the function $f ( x ) = 4 ^ { - x }$

Accepted Answer

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

Evaluate without the use of a calculator. $\log _ { 4 } 4$

Expand into a sum and/or difference of logarithms. Assume all variables represent positive real numbers. $\log _ { 7 } x ^ { y }$

Write the expression as a single logarithm. Assume all variables represent positive real numbers. $\frac { 1 } { 3 } \ln a - 6 \ln b - \frac { 14 } { 3 } \ln c$

Find the value of $\log _ { b } 12$ , given that $\log _ { b } 3 = 1.025$ and $\log _ { b } 4 = 1.294$ .

Which is a logarithmic function?

If $m ( x ) = x + 4$ and $n ( x ) = \frac { 1 } { x + 9 }$ find the function value, if possible. $( n \circ m ) ( - 9 )$

Solve the logarithmic equation. $\log _ { 6 } t ^ { 4 } = \log _ { 6 } t ^ { 3 } - 2$

Given that $f ( x ) = 2 x ^ { 2 } + 5$ and $g ( x ) = 4 x + 9$ a. find $( f \circ g ) ( x )$ b. find $( g \circ f ) ( x )$

Write an equation of the inverse for the one-to-one function as defined. $z ( x ) = \frac { 1 } { 5 } x - 2$

Expand into sums and/or differences of logarithms. Assume all variables represent positive real numbers. $\log \left( \frac { \sqrt [ 3 ] { a b } } { c ^ { 2 } } \right)$

Simplify the expression. Assume all variables represent positive real numbers. $7 e ^ { \ln ( 1 - y ) }$

Solve the equation. $4 ^ { y } = 64$

Solve the logarithmic equation. $\log _ { 4 } ( c + 7 ) = 3$

Write the expression as a single logarithm. Assume all variables represent positive real numbers. $\frac { 1 } { 3 } \left[ \log \left( a ^ { 2 } + 2 a \right) - \log ( a + 2 ) \right]$

Solve the exponential equation by taking the logarithm of both sides. $15 e ^ { 0.03 m } = 75$

Graph the function $f ( x ) = 3 ^ { x }$ . Plot at least three points.

Approximate the function value from the graph. $(f-g)(0)$

Graph the equation by completing the table and plotting points. Round to two decimal places when necessary. $f(x)=3 e^{x}$ x y -2 0 1

Graph the function $f ( x ) = 4 ^ { - x }$

Linear Equations and Inequalities in One Variable

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Systems of Linear Equations and Inequalities

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Exam 8: Exponential and Logarithmic Functions and Applications

Evaluate without the use of a calculator. log⁡44\log _ { 4 } 4log4​4

Expand into a sum and/or difference of logarithms. Assume all variables represent positive real numbers. log⁡7xy\log _ { 7 } x ^ { y }log7​xy

Write the expression as a single logarithm. Assume all variables represent positive real numbers. 13ln⁡a−6ln⁡b−143ln⁡c\frac { 1 } { 3 } \ln a - 6 \ln b - \frac { 14 } { 3 } \ln c31​lna−6lnb−314​lnc

Find the value of log⁡b12\log _ { b } 12logb​12 , given that log⁡b3=1.025\log _ { b } 3 = 1.025logb​3=1.025 and log⁡b4=1.294\log _ { b } 4 = 1.294logb​4=1.294 .

Which is a logarithmic function?

If m(x)=x+4m ( x ) = x + 4m(x)=x+4 and n(x)=1x+9n ( x ) = \frac { 1 } { x + 9 }n(x)=x+91​ find the function value, if possible. (n∘m)(−9)( n \circ m ) ( - 9 )(n∘m)(−9)

Solve the logarithmic equation. log⁡6t4=log⁡6t3−2\log _ { 6 } t ^ { 4 } = \log _ { 6 } t ^ { 3 } - 2log6​t4=log6​t3−2

Given that f(x)=2x2+5f ( x ) = 2 x ^ { 2 } + 5f(x)=2x2+5 and g(x)=4x+9g ( x ) = 4 x + 9g(x)=4x+9 a. find (f∘g)(x)( f \circ g ) ( x )(f∘g)(x) b. find (g∘f)(x)( g \circ f ) ( x )(g∘f)(x)

Write an equation of the inverse for the one-to-one function as defined. z(x)=15x−2z ( x ) = \frac { 1 } { 5 } x - 2z(x)=51​x−2

Expand into sums and/or differences of logarithms. Assume all variables represent positive real numbers. log⁡(ab3c2)\log \left( \frac { \sqrt [ 3 ] { a b } } { c ^ { 2 } } \right)log(c23ab​​)

Simplify the expression. Assume all variables represent positive real numbers. 7eln⁡(1−y)7 e ^ { \ln ( 1 - y ) }7eln(1−y)

Solve the equation. 4y=644 ^ { y } = 644y=64

Solve the logarithmic equation. log⁡4(c+7)=3\log _ { 4 } ( c + 7 ) = 3log4​(c+7)=3

Write the expression as a single logarithm. Assume all variables represent positive real numbers. 13[log⁡(a2+2a)−log⁡(a+2)]\frac { 1 } { 3 } \left[ \log \left( a ^ { 2 } + 2 a \right) - \log ( a + 2 ) \right]31​[log(a2+2a)−log(a+2)]

Solve the exponential equation by taking the logarithm of both sides. 15e0.03m=7515 e ^ { 0.03 m } = 7515e0.03m=75

Graph the function f(x)=3xf ( x ) = 3 ^ { x }f(x)=3x . Plot at least three points.

Approximate the function value from the graph. (f−g)(0)(f-g)(0)(f−g)(0)

Graph the equation by completing the table and plotting points. Round to two decimal places when necessary. f(x)=3exf(x)=3 e^{x}f(x)=3ex x y -2 0 1

Graph the function f(x)=4−xf ( x ) = 4 ^ { - x }f(x)=4−x

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables and Functions

Systems of Linear Equations and Inequalities

Polynomials

Rational Expressions and Rational Equations

Radicals and Complex Numbers

Quadratic Equations, Functions and Inequalities

Conic Sections

Binomial Expansions, Sequences, and Series

Online: Transformations, Piecewise-Defined Functions, and Probability

Filters

Evaluate without the use of a calculator. $\log _ { 4 } 4$

Expand into a sum and/or difference of logarithms. Assume all variables represent positive real numbers. $\log _ { 7 } x ^ { y }$

Write the expression as a single logarithm. Assume all variables represent positive real numbers. $\frac { 1 } { 3 } \ln a - 6 \ln b - \frac { 14 } { 3 } \ln c$

Find the value of $\log _ { b } 12$ , given that $\log _ { b } 3 = 1.025$ and $\log _ { b } 4 = 1.294$ .

If $m ( x ) = x + 4$ and $n ( x ) = \frac { 1 } { x + 9 }$ find the function value, if possible. $( n \circ m ) ( - 9 )$

Solve the logarithmic equation. $\log _ { 6 } t ^ { 4 } = \log _ { 6 } t ^ { 3 } - 2$

Given that $f ( x ) = 2 x ^ { 2 } + 5$ and $g ( x ) = 4 x + 9$ a. find $( f \circ g ) ( x )$ b. find $( g \circ f ) ( x )$

Write an equation of the inverse for the one-to-one function as defined. $z ( x ) = \frac { 1 } { 5 } x - 2$

Expand into sums and/or differences of logarithms. Assume all variables represent positive real numbers. $\log \left( \frac { \sqrt [ 3 ] { a b } } { c ^ { 2 } } \right)$

Simplify the expression. Assume all variables represent positive real numbers. $7 e ^ { \ln ( 1 - y ) }$

Solve the equation. $4 ^ { y } = 64$

Solve the logarithmic equation. $\log _ { 4 } ( c + 7 ) = 3$

Write the expression as a single logarithm. Assume all variables represent positive real numbers. $\frac { 1 } { 3 } \left[ \log \left( a ^ { 2 } + 2 a \right) - \log ( a + 2 ) \right]$

Solve the exponential equation by taking the logarithm of both sides. $15 e ^ { 0.03 m } = 75$

Graph the function $f ( x ) = 3 ^ { x }$ . Plot at least three points.

Approximate the function value from the graph. $(f-g)(0)$

Graph the equation by completing the table and plotting points. Round to two decimal places when necessary. $f(x)=3 e^{x}$ x y -2 0 1

Graph the function $f ( x ) = 4 ^ { - x }$