Question 1

Use the quotient property of logarithms to write the logarithm as a difference of logarithms. Then
simplify if possible.
-$\log \left( \frac { m ^ { 4 } + n } { 1,000 } \right)$

Accepted Answer

A)  $4 - 4 \log m \cdot \log n$ 
B)  $4 \log m + \log n - 3$ 
C)  $4 \log m \cdot \log n - 4$ 
D)  $\log \left( m ^ { 4 } + n \right) - 3$

Question 2

Determine if the statement is true or false.
-$\log e = \frac { 1 } { \ln 10 }$

Accepted Answer

A) True 
 B)False

Question 3

Choose the one alternative that best completes the statement or answers the question.
Solve for the indicated variable.
-$\ln \left( \frac { k } { A } \right) = \frac { - E } { R T }$ for $k$

Accepted Answer

A)  $k = A e ^ { - E / ( R T ) }$ 
B)  $k = - A e ^ { E / ( R T ) }$ 
C)  $k = \frac { e ^ { - E / ( R T ) } } { A }$ 
D)  $k = A \ln \left( \frac { - E } { R T } \right)$

Question 4

The graph of a function is given. Graph the inverse function.
-

Accepted Answer

A) 
 
B) 
. 
C) 
 
D)

Question 5

Use the change-of-base and a calculator to approximate the logarithm to 4 decimal places.
-$$\log _ { 8 } \left( 7.32 \cdot 10 ^ { - 7 } \right)$$

Accepted Answer

A)  $- 6.7939$ 
B)  $- 6.1355$ 
C)  $- 0.1472$ 
D)  $- 1.7659$

Question 6

Write the word or phrase that best completes each statement or answers the question.
-$$\log _ { 8 } \frac { 1 } { 512 } = - 3$$

Accepted Answer

A)  $\frac { 1 } { 512 } = 3 ^ { - 8 }$ 
B)  $\left( \frac { 1 } { 512 } \right) ^ { - 3 } = 8$ 
C)  $8 ^ { - 3 } = \frac { 1 } { 512 }$ 
D)  $\frac { 1 } { 512 } = - 3 ^ { 8 }$

Question 7

Determine if the relation defines y as a one-to-one function of x.
-

Accepted Answer

A)  Yes 
B)  No

Question 8

Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible.
-$\log _ { 2 } \frac { p ^ { 5 } } { q ^ { 9 } }$

Accepted Answer

A)  $\frac { 5 } { 9 } \left( \log _ { 2 } p - \log _ { 2 } q \right)$ 
B)  $\frac { 5 } { 9 } \left( \log _ { 2 } p + \log _ { 2 } q \right)$ 
C)  $- 4 \left( \log _ { 2 } p - \log _ { 2 } q \right)$ 
D)  $5 \log _ { 2 } p - 9 \log _ { 2 } q$

Question 9

ng, in
-The population of bacteria culture was 2000 at noon, and was increasing at a rate of $10 \%$ per hour. The number can be found using the function
$$P ( t ) = 2,000 ( 1.1 ) ^ { t }$$
where $t$ is the number of hours past noon. Predict the population 11 hours later, at $11 \mathrm { PM }$ to the nearest whole number.

Accepted Answer

A)  24,200 
B)  5,706 
C)  3,706 
D)  7,726

Question 10

A one-to-one function is given. Write an expression for the inverse function.
-$$m ( x ) = 7 x ^ { 3 } + 2$$

Accepted Answer

A)  $m ^ { - 1 } ( x ) = \frac { x - 2 } { 7 }$ 
B)  $m ^ { - 1 } ( x ) = \frac { x + 2 } { 7 }$ 
C)  $m ^ { - 1 } ( x ) = \left( \frac { x + 2 } { 7 } \right) ^ { 3 }$ 
D)  $m ^ { - 1 } ( x ) = \sqrt [ 3 ] { \frac { x - 2 } { 7 } }$

Question 11

Find an equation for the inverse function.
-$$f ( x ) = \log ( x + 5 ) + 4$$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = 10 ^ { x + 4 } + 5$ 
B)  $f ^ { - 1 } ( x ) = 10 ^ { x + 5 } + 4$ 
C)  $f ^ { - 1 } ( x ) = 10 ^ { x - 4 } - 5$ 
D)  $f ^ { - 1 } ( x ) = 10 ^ { x - 5 } - 4$

Question 12

The graph of a function is given. Graph the inverse function.
-

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

Question 13

A one-to-one function is given. Write an expression for the inverse function.
-$$f ( x ) = \sqrt [ 3 ] { x + 7 }$$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = ( x + 7 ) ^ { 3 }$ 
B)  $f ^ { - 1 } ( x ) = x ^ { 3 } - 7$ 
C)  $f ^ { - 1 } ( x ) = x ^ { 3 } + 7$ 
D)  $f ^ { - 1 } ( x ) = ( x - 7 ) ^ { 3 }$

Question 14

Write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as
possible.
-$$\frac { 1 } { 2 } \log _ { 2 } p + 4 \log _ { 2 } 3$$

Accepted Answer

A)  $\log _ { 2 } ( \sqrt { p } + 81 )$ 
B)  $\log _ { 2 } \frac { p + 24 } { 2 }$ 
C)  $\log _ { 2 } ( 81 \sqrt { p } )$ 
D)  $\log _ { 2 } 6 p$

Question 15

Write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as
possible.
-$$\frac { 1 } { 2 } [ 6 \ln ( x - 3 ) + \ln x - 2 \ln x ]$$

Accepted Answer

A)  $\ln \left[ \frac { ( x - 3 ) ^ { 3 } } { x } \right]$ 
B)  $\ln \left[ \frac { ( x - 3 ) ^ { 6 } } { 2 x } \right]$ 
C)  $\ln \left[ \frac { ( x - 3 ) ^ { 3 } } { \sqrt { x } } \right]$ 
D)  $\ln \left[ \frac { \sqrt { x } ( x - 3 ) ^ { 3 } } { 2 x } \right]$

Question 16

Graph the function and write the domain and range in interval notation.
-$$f ( x ) = \left( \frac { 3 } { 2 } \right) ^ { x }$$

Accepted Answer

A)

Domain: $( - \infty , \infty )$
Range: $( 0 , \infty )$ 
B)

Domain: $( 0 , \infty )$
Range: $( - \infty , \infty )$ 
C)

Domain: $( - \infty , \infty )$
Range: $( 0 , \infty )$ 
D)

Domain: $( 0 , \infty )$
Range: $( - \infty , \infty )$

Question 17

Simplify the expression.
-$$3 ^ { \log _ { 3 } ( 4 x + 4 y ) }$$

Accepted Answer

A)  $\frac { 8 } { 3 }$ 
B)  $( 4 x + 4 y ) ^ { 3 }$ 
C)  $12 x + 12 y$ 
D)  $4 x + 4 y$

Question 18

Choose the one alternative that best completes the statement or answers the question.
Solve for the indicated variable.
-$A = P ( 1 + r ) ^ { t }$ for $\mathrm { t }$

Accepted Answer

A)  $t = \frac { \ln \left( \frac { A } { P } \right) } { 1 + r }$ 
B)  $t = \frac { \ln \left( \frac { A } { P } \right) } { \ln ( 1 + r ) }$ 
C)  $t = \frac { \ln ( A - P ) } { \ln ( 1 + r ) }$ 
D)  $t = \frac { \ln ( P - A ) } { \ln ( 1 + r ) }$

Question 19

Solve the problem.
-A $\$ 3,000$ bond grows to $\$ 4,475.47$ in 8 yr under continuous compounding. Find the interest rate. Round our answer to the nearest whole percent.

Accepted Answer

A)  $8 \%$ 
B)  $5 \%$ 
C)  $7 \%$ 
D)  $6 \%$

Question 20

Simplify the expression.
-$\log _ { 7 } \left( \frac { 1 } { 49 } \right)$

Accepted Answer

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

Exam 4: Exponential and Logarithmic Functions

Use the quotient property of logarithms to write the logarithm as a difference of logarithms. Then simplify if possible. - $\log \left( \frac { m ^ { 4 } + n } { 1,000 } \right)$

Determine if the statement is true or false. - $\log e = \frac { 1 } { \ln 10 }$

Choose the one alternative that best completes the statement or answers the question. Solve for the indicated variable. - $\ln \left( \frac { k } { A } \right) = \frac { - E } { R T }$ for $k$

The graph of a function is given. Graph the inverse function. -

Use the change-of-base and a calculator to approximate the logarithm to 4 decimal places. - $\log _ { 8 } \left( 7.32 \cdot 10 ^ { - 7 } \right)$

Write the word or phrase that best completes each statement or answers the question. - $\log _ { 8 } \frac { 1 } { 512 } = - 3$

Determine if the relation defines y as a one-to-one function of x. -

Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible. - $\log _ { 2 } \frac { p ^ { 5 } } { q ^ { 9 } }$

A one-to-one function is given. Write an expression for the inverse function. - $m ( x ) = 7 x ^ { 3 } + 2$

Find an equation for the inverse function. - $f ( x ) = \log ( x + 5 ) + 4$

The graph of a function is given. Graph the inverse function. -

A one-to-one function is given. Write an expression for the inverse function. - $f ( x ) = \sqrt [ 3 ] { x + 7 }$

Write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as possible. - $\frac { 1 } { 2 } \log _ { 2 } p + 4 \log _ { 2 } 3$

Write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as possible. - $\frac { 1 } { 2 } [ 6 \ln ( x - 3 ) + \ln x - 2 \ln x ]$

Graph the function and write the domain and range in interval notation. - $f ( x ) = \left( \frac { 3 } { 2 } \right) ^ { x }$

Simplify the expression. - $3 ^ { \log _ { 3 } ( 4 x + 4 y ) }$

Choose the one alternative that best completes the statement or answers the question. Solve for the indicated variable. - $A = P ( 1 + r ) ^ { t }$ for $\mathrm { t }$

Solve the problem. -A $\$ 3,000$ bond grows to $\$ 4,475.47$ in 8 yr under continuous compounding. Find the interest rate. Round our answer to the nearest whole percent.

Simplify the expression. - $\log _ { 7 } \left( \frac { 1 } { 49 } \right)$

Exam 4: Exponential and Logarithmic Functions

Use the quotient property of logarithms to write the logarithm as a difference of logarithms. Then simplify if possible. - log⁡(m4+n1,000) \log \left( \frac { m ^ { 4 } + n } { 1,000 } \right) log(1,000m4+n​)

Determine if the statement is true or false. - log⁡e=1ln⁡10\log e = \frac { 1 } { \ln 10 }loge=ln101​

Choose the one alternative that best completes the statement or answers the question. Solve for the indicated variable. - ln⁡(kA) =−ERT\ln \left( \frac { k } { A } \right) = \frac { - E } { R T }ln(Ak​) =RT−E​ for kkk

The graph of a function is given. Graph the inverse function. -

Use the change-of-base and a calculator to approximate the logarithm to 4 decimal places. - log⁡8(7.32⋅10−7) \log _ { 8 } \left( 7.32 \cdot 10 ^ { - 7 } \right) log8​(7.32⋅10−7)

Write the word or phrase that best completes each statement or answers the question. - log⁡81512=−3\log _ { 8 } \frac { 1 } { 512 } = - 3log8​5121​=−3

Determine if the relation defines y as a one-to-one function of x. -

Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible. - log⁡2p5q9\log _ { 2 } \frac { p ^ { 5 } } { q ^ { 9 } }log2​q9p5​

A one-to-one function is given. Write an expression for the inverse function. - m(x) =7x3+2m ( x ) = 7 x ^ { 3 } + 2m(x) =7x3+2

Find an equation for the inverse function. - f(x) =log⁡(x+5) +4f ( x ) = \log ( x + 5 ) + 4f(x) =log(x+5) +4

The graph of a function is given. Graph the inverse function. -

A one-to-one function is given. Write an expression for the inverse function. - f(x) =x+73f ( x ) = \sqrt [ 3 ] { x + 7 }f(x) =3x+7​

Write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as possible. - 12log⁡2p+4log⁡23\frac { 1 } { 2 } \log _ { 2 } p + 4 \log _ { 2 } 321​log2​p+4log2​3

Write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as possible. - 12[6ln⁡(x−3) +ln⁡x−2ln⁡x]\frac { 1 } { 2 } [ 6 \ln ( x - 3 ) + \ln x - 2 \ln x ]21​[6ln(x−3) +lnx−2lnx]

Graph the function and write the domain and range in interval notation. - f(x) =(32) xf ( x ) = \left( \frac { 3 } { 2 } \right) ^ { x }f(x) =(23​) x

Simplify the expression. - 3log⁡3(4x+4y) 3 ^ { \log _ { 3 } ( 4 x + 4 y ) }3log3​(4x+4y)

Choose the one alternative that best completes the statement or answers the question. Solve for the indicated variable. - A=P(1+r) tA = P ( 1 + r ) ^ { t }A=P(1+r) t for t\mathrm { t }t

Solve the problem. -A $3,000\$ 3,000$3,000 bond grows to $4,475.47\$ 4,475.47$4,475.47 in 8 yr under continuous compounding. Find the interest rate. Round our answer to the nearest whole percent.

Simplify the expression. - log⁡7(149) \log _ { 7 } \left( \frac { 1 } { 49 } \right) log7​(491​)

Use the quotient property of logarithms to write the logarithm as a difference of logarithms. Then simplify if possible. - $\log \left( \frac { m ^ { 4 } + n } { 1,000 } \right)$

Determine if the statement is true or false. - $\log e = \frac { 1 } { \ln 10 }$

Choose the one alternative that best completes the statement or answers the question. Solve for the indicated variable. - $\ln \left( \frac { k } { A } \right) = \frac { - E } { R T }$ for $k$

Use the change-of-base and a calculator to approximate the logarithm to 4 decimal places. - $\log _ { 8 } \left( 7.32 \cdot 10 ^ { - 7 } \right)$

Write the word or phrase that best completes each statement or answers the question. - $\log _ { 8 } \frac { 1 } { 512 } = - 3$

Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible. - $\log _ { 2 } \frac { p ^ { 5 } } { q ^ { 9 } }$

A one-to-one function is given. Write an expression for the inverse function. - $m ( x ) = 7 x ^ { 3 } + 2$

Find an equation for the inverse function. - $f ( x ) = \log ( x + 5 ) + 4$

A one-to-one function is given. Write an expression for the inverse function. - $f ( x ) = \sqrt [ 3 ] { x + 7 }$

Write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as possible. - $\frac { 1 } { 2 } \log _ { 2 } p + 4 \log _ { 2 } 3$

Write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as possible. - $\frac { 1 } { 2 } [ 6 \ln ( x - 3 ) + \ln x - 2 \ln x ]$

Graph the function and write the domain and range in interval notation. - $f ( x ) = \left( \frac { 3 } { 2 } \right) ^ { x }$

Simplify the expression. - $3 ^ { \log _ { 3 } ( 4 x + 4 y ) }$

Choose the one alternative that best completes the statement or answers the question. Solve for the indicated variable. - $A = P ( 1 + r ) ^ { t }$ for $\mathrm { t }$

Solve the problem. -A $\$ 3,000$ bond grows to $\$ 4,475.47$ in 8 yr under continuous compounding. Find the interest rate. Round our answer to the nearest whole percent.

Simplify the expression. - $\log _ { 7 } \left( \frac { 1 } { 49 } \right)$