Question 1

Which of the following specifies a one-to-one function?

Accepted Answer

A)  h = {(1,1), (2,2), (3,1)} 
B)  f = {(0,1), (0,2), (1,3)} 
C)  g = {(1,1), (2,2), (3,2)} 
D)  None of the above are one-to-one functions. 
A)  h = {(1,1), (2,2), (3,1)} 
B)  f = {(0,1), (0,2), (1,3)} 
C)  g = {(1,1), (2,2), (3,2)} 
D)  None of the above are one-to-one functions.

Question 2

Write the expression as a sum and/or difference of ln a and ln b. Assume all variables represent positive real numbers. $\ln \left( \frac { a } { b } \right) ^ { 6 }$

Accepted Answer

A)  $6 \ln a + 6 \ln b$ 
B)  $6 \ln \left( \frac { a } { b } \right)$ 
C)  $\ln a ^ { 2 } - \ln b ^ { 2 }$ 
D)  $6 \ln a - 6 \ln b$ 
A)  $6 \ln a + 6 \ln b$ 
B)  $6 \ln \left( \frac { a } { b } \right)$ 
C)  $\ln a ^ { 2 } - \ln b ^ { 2 }$ 
D)  $6 \ln a - 6 \ln b$

Question 3

Identify the domain of the function. $f ( x ) = 3.8 \ln ( x + 1 )$

Accepted Answer

A)  $( 0 , \infty )$ 
B)  $( - \infty , \infty )$ 
C)  $( - 1 , \infty )$ 
D)  $( - \infty , 1 )$ 
A)  $( 0 , \infty )$ 
B)  $( - \infty , \infty )$ 
C)  $( - 1 , \infty )$ 
D)  $( - \infty , 1 )$

Question 4

The level of a sound in decibels is calculated using the formula $D = 10 \cdot \log \left( I \times 10 ^ { 12 } \right)$ where I is the intensity of the sound waves in watts per square meter. A jackhammer puts out 1 watt per square meter. How many decibels is that?

Accepted Answer

A)  12 
B)  10 
C)  120 
D)  1200 
A)  12 
B)  10 
C)  120 
D)  1200

Question 5

Write the equation in logarithmic form. $$4 ^ { 3 } = 64$$

Accepted Answer

A)  $\log _ { 4 } 64 = 3$ 
B)  $\log _ { 64 } 4 = 3$ 
C)  $\log _ { 3 } 4 = 64$ 
D)  $\log _ { 4 } 3 = 64$ 
A)  $\log _ { 4 } 64 = 3$ 
B)  $\log _ { 64 } 4 = 3$ 
C)  $\log _ { 3 } 4 = 64$ 
D)  $\log _ { 4 } 3 = 64$

Question 6

Write the equation in exponential form. $$\log _ { 4 } 4096 = 6$$

Accepted Answer

A)  $4 ^ { 6 } = 4096$ 
B)  $6 ^ { 4096 } = 4$ 
C)  $6 ^ { 4 } = 4096$ 
D)  $4096 ^ { 6 } = 4$ 
A)  $4 ^ { 6 } = 4096$ 
B)  $6 ^ { 4096 } = 4$ 
C)  $6 ^ { 4 } = 4096$ 
D)  $4096 ^ { 6 } = 4$

Question 7

Determine if the function is one-to-one by using the horizontal line test.

Accepted Answer

A)  No, because the line y = x intersects the curve at more than one point. 
B)  No, because the line y = -1 intersects the curve at more than one point. 
C)  No, because the line x = -1 intersects the curve at more than one point. 
D)  Yes 
A)  No, because the line y = x intersects the curve at more than one point. 
B)  No, because the line y = -1 intersects the curve at more than one point. 
C)  No, because the line x = -1 intersects the curve at more than one point. 
D)  Yes

Question 8

Simplify the expression. Assume all variables represent positive real numbers. $\ln \left( e ^ { - 9 x ^ { 2 } + 19 x } \right)$

Accepted Answer

A)  $- 9 x ^ { 2 } + 19 x$ 
B)  $19 x \cdot \ln \left( e ^ { - 9 x ^ { 2 } } \right)$ 
C)  $1 ^ { - 9 x ^ { 2 } + 19 x }$ 
D)  $e ^ { - 9 x ^ { 2 } + 19 x }$ 
A)  $- 9 x ^ { 2 } + 19 x$ 
B)  $19 x \cdot \ln \left( e ^ { - 9 x ^ { 2 } } \right)$ 
C)  $1 ^ { - 9 x ^ { 2 } + 19 x }$ 
D)  $e ^ { - 9 x ^ { 2 } + 19 x }$

Question 9

Find the domain of the function and express the domain in interval notation. $$y ( x ) = \log \left( x ^ { 2 } - 10 x + 25 \right)$$

Accepted Answer

The answer of Find the domain of the function and...

Question 10

Write the equation in logarithmic form. $$5 ^ { - 5 } = \frac { 1 } { 3125 }$$

Accepted Answer

A)  $\log _ { 5 } \frac { 1 } { 3125 } = - 5$ 
B)  $\log _ { - 5 } 5 = 3125$ 
C)  $\log _ { 5 } ( - 5 ) = 3125$ 
D)  $- \log _ { 5 } 3125 = - 5$ 
A)  $\log _ { 5 } \frac { 1 } { 3125 } = - 5$ 
B)  $\log _ { - 5 } 5 = 3125$ 
C)  $\log _ { 5 } ( - 5 ) = 3125$ 
D)  $- \log _ { 5 } 3125 = - 5$

Question 11

Expand into a sum and/or difference of logarithms of a and b. Assume all variables represent positive real numbers. $\log _ { 8 } \left( \frac { a ^ { 4 } } { \sqrt { b } } \right)$

Accepted Answer

A)  $4 \log _ { 8 } a - \frac { 1 } { 2 } \log _ { 8 } b$ 
B)  $\frac { \log _ { 8 } a ^ { 4 } } { \frac { 1 } { 2 } \log _ { 8 } b }$ 
C)  $\log _ { 8 } 4 a + \log _ { 8 } \frac { b } { 2 }$ 
D)  $4 \log _ { 8 } a + \frac { 1 } { 2 } \log _ { 8 } b$ 
A)  $4 \log _ { 8 } a - \frac { 1 } { 2 } \log _ { 8 } b$ 
B)  $\frac { \log _ { 8 } a ^ { 4 } } { \frac { 1 } { 2 } \log _ { 8 } b }$ 
C)  $\log _ { 8 } 4 a + \log _ { 8 } \frac { b } { 2 }$ 
D)  $4 \log _ { 8 } a + \frac { 1 } { 2 } \log _ { 8 } b$

Question 12

Expand into a sum and/or difference of logarithms. Assume all variables represent positive real numbers. $\log \left( \frac { x } { y } \right)$

Accepted Answer

A)  $\log x + \log y$ 
B)  $\log x \cdot \log y ^ { - 1 }$ 
C)  $\log x - \log y$ 
D)  $\frac { \log x } { \log y }$ 
A)  $\log x + \log y$ 
B)  $\log x \cdot \log y ^ { - 1 }$ 
C)  $\log x - \log y$ 
D)  $\frac { \log x } { \log y }$

Question 13

Write the expression as a sum and/or difference of ln x and ln y. Assume all variables represent positive real numbers. $\ln \left( \frac { e ^ { 2 } x } { y } \right)$

Accepted Answer

A)  $2 + \ln x - \ln y$ 
B)  $\frac { 2 \ln x } { \ln y }$ 
C)  $\ln e ^ { x } x - \ln y$ 
D)  $\ln e ^ { x } - \ln x - \ln y$ 
A)  $2 + \ln x - \ln y$ 
B)  $\frac { 2 \ln x } { \ln y }$ 
C)  $\ln e ^ { x } x - \ln y$ 
D)  $\ln e ^ { x } - \ln x - \ln y$

Question 14

The decibel scale measures the loudness of sounds based on the intensity of sound waves. Decibels can be calculated using the formula $D = 10 \log \left( \frac { I } { 10 ^ { - 12 } } \right)$ where I is the intensity of a sound wave in watts per meter. What is the intensity of a shout that registers 85 decibels? Round to six decimal places.

Accepted Answer

0.000316 w

Question 15

$$\text { For } f ( x ) = 2 ^ { x } \text {, find for } f ( 5 ) \text { and } f ( - 6 )$$

Accepted Answer

The answer of \[\text { For } f ( x...

Question 16

Solve the logarithmic equation. $\ln y ^ { 2 } = 10$

Accepted Answer

A)  $\{ \ln 2 , - \ln 2 \}$ 
B)  $\left\{ \frac { e } { 5 } \right\}$ 
C)  $\left\{ e ^ { 5 } , - e ^ { 5 } \right\}$ 
D)  $\left\{ \frac { \sqrt { 10 } } { \ln } , - \frac { \sqrt { 10 } } { \ln } \right\}$ 
A)  $\{ \ln 2 , - \ln 2 \}$ 
B)  $\left\{ \frac { e } { 5 } \right\}$ 
C)  $\left\{ e ^ { 5 } , - e ^ { 5 } \right\}$ 
D)  $\left\{ \frac { \sqrt { 10 } } { \ln } , - \frac { \sqrt { 10 } } { \ln } \right\}$

Question 17

If $m ( x ) = x ^ { 3 }$ and $n ( x ) = \sqrt { 6 + x }$ find the function value, if possible. $( m - n ) ( - 5 )$

Accepted Answer

A)  $- 126$ 
B)  124 
C)  $- 124$ 
D)  Not a real number 
A)  $- 126$ 
B)  124 
C)  $- 124$ 
D)  Not a real number

Question 18

The enrollment at one Midwestern college is approximated by the formula $P = 3000 ( 1.08 ) ^ { t }$ where t is the number of years after 2000. What is the first year in which you would expect enrollment to surpass 4900?

Accepted Answer

The answer of The enrollment at one Midwestern college is...

Question 19

Solve the exponential equation by taking a logarithm of both sides. $$10 ^ { x } = 0.0185$$

Accepted Answer

A)  $\log 0.0185$ 
B)  $\ln 0.0185$ 
C)  $1.0435$ 
D)  $0.0185$ 
A)  $\log 0.0185$ 
B)  $\ln 0.0185$ 
C)  $1.0435$ 
D)  $0.0185$

Question 20

Use the change-of-base formula to approximate the logarithm to four decimal places. $$\log _ { 5 } 7.3$$

Accepted Answer

A)  0.8096 
B)  0.1644 
C)  1.2351 
D)  0.8633 
A)  0.8096 
B)  0.1644 
C)  1.2351 
D)  0.8633

Which of the following specifies a one-to-one function?

Write the expression as a sum and/or difference of ln a and ln b. Assume all variables represent positive real numbers. $\ln \left( \frac { a } { b } \right) ^ { 6 }$

Identify the domain of the function. $f ( x ) = 3.8 \ln ( x + 1 )$

The level of a sound in decibels is calculated using the formula $D = 10 \cdot \log \left( I \times 10 ^ { 12 } \right)$ where I is the intensity of the sound waves in watts per square meter. A jackhammer puts out 1 watt per square meter. How many decibels is that?

Write the equation in logarithmic form. $4 ^ { 3 } = 64$

Write the equation in exponential form. $\log _ { 4 } 4096 = 6$

Determine if the function is one-to-one by using the horizontal line test.

Simplify the expression. Assume all variables represent positive real numbers. $\ln \left( e ^ { - 9 x ^ { 2 } + 19 x } \right)$

Find the domain of the function and express the domain in interval notation. $y ( x ) = \log \left( x ^ { 2 } - 10 x + 25 \right)$

Write the equation in logarithmic form. $5 ^ { - 5 } = \frac { 1 } { 3125 }$

Expand into a sum and/or difference of logarithms of a and b. Assume all variables represent positive real numbers. $\log _ { 8 } \left( \frac { a ^ { 4 } } { \sqrt { b } } \right)$

Expand into a sum and/or difference of logarithms. Assume all variables represent positive real numbers. $\log \left( \frac { x } { y } \right)$

Write the expression as a sum and/or difference of ln x and ln y. Assume all variables represent positive real numbers. $\ln \left( \frac { e ^ { 2 } x } { y } \right)$

$\text { For } f ( x ) = 2 ^ { x } \text {, find for } f ( 5 ) \text { and } f ( - 6 )$

Solve the logarithmic equation. $\ln y ^ { 2 } = 10$

If $m ( x ) = x ^ { 3 }$ and $n ( x ) = \sqrt { 6 + x }$ find the function value, if possible. $( m - n ) ( - 5 )$

The enrollment at one Midwestern college is approximated by the formula $P = 3000 ( 1.08 ) ^ { t }$ where t is the number of years after 2000. What is the first year in which you would expect enrollment to surpass 4900?

Solve the exponential equation by taking a logarithm of both sides. $10 ^ { x } = 0.0185$

Use the change-of-base formula to approximate the logarithm to four decimal places. $\log _ { 5 } 7.3$

Linear Equations and Inequalities in One Variable

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Exam 8: Exponential and Logarithmic Functions and Applications

Which of the following specifies a one-to-one function?

Write the expression as a sum and/or difference of ln a and ln b. Assume all variables represent positive real numbers. ln⁡(ab)6\ln \left( \frac { a } { b } \right) ^ { 6 }ln(ba​)6

Identify the domain of the function. f(x)=3.8ln⁡(x+1)f ( x ) = 3.8 \ln ( x + 1 )f(x)=3.8ln(x+1)

Write the equation in logarithmic form. 43=644 ^ { 3 } = 6443=64

Write the equation in exponential form. log⁡44096=6\log _ { 4 } 4096 = 6log4​4096=6

Determine if the function is one-to-one by using the horizontal line test.

Simplify the expression. Assume all variables represent positive real numbers. ln⁡(e−9x2+19x)\ln \left( e ^ { - 9 x ^ { 2 } + 19 x } \right)ln(e−9x2+19x)

Find the domain of the function and express the domain in interval notation. y(x)=log⁡(x2−10x+25)y ( x ) = \log \left( x ^ { 2 } - 10 x + 25 \right)y(x)=log(x2−10x+25)

Write the equation in logarithmic form. 5−5=131255 ^ { - 5 } = \frac { 1 } { 3125 }5−5=31251​

Expand into a sum and/or difference of logarithms of a and b. Assume all variables represent positive real numbers. log⁡8(a4b)\log _ { 8 } \left( \frac { a ^ { 4 } } { \sqrt { b } } \right)log8​(b​a4​)

Expand into a sum and/or difference of logarithms. Assume all variables represent positive real numbers. log⁡(xy)\log \left( \frac { x } { y } \right)log(yx​)

Write the expression as a sum and/or difference of ln x and ln y. Assume all variables represent positive real numbers. ln⁡(e2xy)\ln \left( \frac { e ^ { 2 } x } { y } \right)ln(ye2x​)

For f(x)=2x, find for f(5) and f(−6)\text { For } f ( x ) = 2 ^ { x } \text {, find for } f ( 5 ) \text { and } f ( - 6 ) For f(x)=2x, find for f(5) and f(−6)

Solve the logarithmic equation. ln⁡y2=10\ln y ^ { 2 } = 10lny2=10

If m(x)=x3m ( x ) = x ^ { 3 }m(x)=x3 and n(x)=6+xn ( x ) = \sqrt { 6 + x }n(x)=6+x​ find the function value, if possible. (m−n)(−5)( m - n ) ( - 5 )(m−n)(−5)

The enrollment at one Midwestern college is approximated by the formula P=3000(1.08)tP = 3000 ( 1.08 ) ^ { t }P=3000(1.08)t where t is the number of years after 2000. What is the first year in which you would expect enrollment to surpass 4900?

Solve the exponential equation by taking a logarithm of both sides. 10x=0.018510 ^ { x } = 0.018510x=0.0185

Use the change-of-base formula to approximate the logarithm to four decimal places. log⁡57.3\log _ { 5 } 7.3log5​7.3

Linear Equations and Inequalities in One Variable

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Online: Transformations, Piecewise-Defined Functions, and Probability

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Write the expression as a sum and/or difference of ln a and ln b. Assume all variables represent positive real numbers. $\ln \left( \frac { a } { b } \right) ^ { 6 }$

Identify the domain of the function. $f ( x ) = 3.8 \ln ( x + 1 )$

Write the equation in logarithmic form. $4 ^ { 3 } = 64$

Write the equation in exponential form. $\log _ { 4 } 4096 = 6$

Simplify the expression. Assume all variables represent positive real numbers. $\ln \left( e ^ { - 9 x ^ { 2 } + 19 x } \right)$

Find the domain of the function and express the domain in interval notation. $y ( x ) = \log \left( x ^ { 2 } - 10 x + 25 \right)$

Write the equation in logarithmic form. $5 ^ { - 5 } = \frac { 1 } { 3125 }$

Expand into a sum and/or difference of logarithms of a and b. Assume all variables represent positive real numbers. $\log _ { 8 } \left( \frac { a ^ { 4 } } { \sqrt { b } } \right)$

Expand into a sum and/or difference of logarithms. Assume all variables represent positive real numbers. $\log \left( \frac { x } { y } \right)$

Write the expression as a sum and/or difference of ln x and ln y. Assume all variables represent positive real numbers. $\ln \left( \frac { e ^ { 2 } x } { y } \right)$

$\text { For } f ( x ) = 2 ^ { x } \text {, find for } f ( 5 ) \text { and } f ( - 6 )$

Solve the logarithmic equation. $\ln y ^ { 2 } = 10$

If $m ( x ) = x ^ { 3 }$ and $n ( x ) = \sqrt { 6 + x }$ find the function value, if possible. $( m - n ) ( - 5 )$

The enrollment at one Midwestern college is approximated by the formula $P = 3000 ( 1.08 ) ^ { t }$ where t is the number of years after 2000. What is the first year in which you would expect enrollment to surpass 4900?

Solve the exponential equation by taking a logarithm of both sides. $10 ^ { x } = 0.0185$

Use the change-of-base formula to approximate the logarithm to four decimal places. $\log _ { 5 } 7.3$