Question 1

Determine the equation of the horizontal asymptote for the graph of this function, and state the domain and range of
this function.
-$$f ( x ) = \log _ { 5 } ( x + 1 ) + 3$$

Accepted Answer

A)  Vertical asymptote: $x = 3$;
Domain: $( 3 , \infty )$, Range: $( - \infty , \infty )$ 
B)  Vertical asymptote: $x = 1$;
Domain: $( 1 , \infty )$, Range: $( - \infty , \infty )$ 
C)  Vertical asymptote: $x = - 1$;
Domain: $( - 1 , \infty )$, Range: $( - \infty , \infty )$ 
D)  Vertical asymptote: $x = 1$;
Domain: $( - 1 , \infty )$, Range: $( - \infty , \infty )$

Question 2

Rewrite as a single logarithm. Assume all variables represent positive real numbers.
-$4 \log _ { 4 } ( 4 x + 2 ) + 3 \log _ { 4 } ( 5 x + 3 )$

Accepted Answer

A)  $12 \log _ { 4 } ( 4 x + 2 ) ( 5 x + 3 )$ 
B)  $\log _ { 4 } \frac { ( 4 x + 2 ) ^ { 4 } } { ( 5 x + 3 ) ^ { 3 } }$ 
C)  $\log _ { 4 } \left( ( 4 x + 2 ) ^ { 4 } ( 5 x + 3 ) ^ { 3 } \right)$ 
D)  $\log _ { 4 } \left( ( 4 x + 2 ) ^ { 4 } + ( 5 x + 3 ) ^ { 3 } \right)$

Question 3

Rewrite as a single logarithm using the quotient rule for logarithms. Assume all variables represent positive real
numbers.
-$$\log _ { b } s - \log _ { b } x$$

Accepted Answer

A)  $\log _ { 2 b } \frac { s } { x }$ 
B)  $\log _ { b } \frac { s } { x }$ 
C)  $\log _ { \mathrm { b } } \mathrm { s } - \mathrm { x }$ 
D)  $\log _ { b } \frac { x } { s }$

Question 4

Expand. Assume that all variables represent positive real numbers.
-$\log _ { \mathrm { b } } \mathrm { yz } 4$

Accepted Answer

A)  $4 \log _ { \mathrm { b } } \mathrm { yz }$ 
B)  $4 \log _ { \mathrm { b } } \mathrm { y } + 4 \log _ { \mathrm { b } } \mathrm { z }$ 
C)  $\log _ { b } y + 4 \log _ { b } z$ 
D)  $\log _ { b } y + \log _ { b } 4 z$

Question 5

Solve the problem.
-The population growth of an animal species is described by F(t) = 300 + 20 log3 (2t + 1), where t is measured in months. Find the population of this species in an area 4 month(s) after the species is
Introduced.

Accepted Answer

A)  260 
B)  180 
C)  340 
D)  480

Question 6

Evaluate the given function.
-$$f ( x ) = 2 ^ { x } , f ( 4 )$$

Accepted Answer

A)  16 
B)  $\frac { 1 } { 2 }$ 
C)  8 
D)  $\frac { 1 } { 8 }$

Question 7

Solve.
-The function A = A0e-0.01155x models the amount in pounds of a particular radioactive material stored in a concrete vault, where x is the number of years since the material was put into the vault.
If 300 pounds of the material are placed in the vault, how much time will need to pass for only 53
Pounds to remain?

Accepted Answer

A)  160 yr 
B)  150 yr 
C)  155 yr 
D)  300 yr

Question 8

Rewrite as the sum of two or more logarithms using the product rule for logarithms. Assume all variables represent
positive real numbers.
-$\log _ { 4 }$ (xy)

Accepted Answer

A)  $\log _ { 2 } x + \log _ { 2 } y$ 
B)  $\log _ { 4 } x - \log _ { 4 } y$ 
C)  $\log _ { 4 } x + \log _ { 4 } y$ 
D)  $\log _ { 2 } x - \log _ { 2 } y$

Question 9

Compute the compound interest.
-How long will it take for $5000 to grow to $15,500 at an interest rate of 3.1% if the interest is compounded quarterly? Round the number of years to the nearest hundredth.

Accepted Answer

A)  37.06 yr 
B)  100.39 yr 
C)  36.64 yr 
D)  146.55 yr

Question 10

Evaluate. Round to the nearest thousandth, if necessary.
-$\log 10,000$

Accepted Answer

A)  5 
B)  $- 4$ 
C)  3 
D)  4

Question 11

Rewrite as a single logarithm. Assume all variables represent positive real numbers.
-$\log \sqrt [ 4 ] { x } + \log x ^ { 4 } - \log x ^ { 3 }$

Accepted Answer

A)  $5 \log x$ 
B)  $11 \log x$ 
C)  $\frac { 5 } { 4 } \log x$ 
D)  $\frac { 3 } { 4 } \log x$

Question 12

Determine the equation of the horizontal asymptote for the graph of this function, and state the domain and range of
this function.
-$$f ( x ) = 5 ^ { x } + 4$$

Accepted Answer

A)  Horizontal asymptote: $y = 0$;
Domain: $( - \infty , \infty )$, Range: $( 0 , \infty )$ 
B)  Horizontal asymptote: $\mathrm { y } = 4$;
Domain: $( - \infty , \infty )$, Range: $( 4 , \infty )$ 
C)  Horizontal asymptote: $\mathrm { y } = 4$;
Domain: $( - \infty , \infty )$, Range: $( - 4 , \infty )$ 
D)  Horizontal asymptote: $\mathrm { y } = - 4$;
Domain: $( - \infty , \infty )$, Range: $( - 4 , \infty )$

Question 13

Evaluate. Round to the nearest thousandth, if necessary.
-$\ln \left( e ^ { - 5 } \right)$

Accepted Answer

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

Question 14

Evaluate the given function.
-$$f ( x ) = 3 ^ { x + 1 } + 3 , f ( 3 )$$

Accepted Answer

A)  84 
B)  3 
C)  6 
D)  30

Question 15

Rewrite in logarithmic form.
-The sales of a new product (in items per month) can be approximated by $$S ( x ) = 300 + 100 \log ( 3 t + 1 )$$

Accepted Answer

A)  500 items per month 
B)  2300 items per month 
C)  1300 items per month 
D)  400 items per month

Question 16

Solve the problem.
-Approximately one-fourth of all glass bottles distributed will be recycled each year. A beverage company distributes 370,000 bottles. The number still in use after t years is given by the function $\mathrm { N } ( \mathrm { t } ) = 370,000 \left( \frac { 1 } { 4 } \right) ^ { \mathrm { t } }$. After how many years will 40,000 bottles still be in use? Round your answer to the nearest tenth.

Accepted Answer

A)  $2.2 \mathrm { yr }$ 
B)  $3.1 \mathrm { yr }$ 
C)  $0.6 \mathrm { yr }$ 
D)  $1.6 \mathrm { yr }$

Question 17

Rewrite as a single logarithm using the quotient rule for logarithms. Assume all variables represent positive real
numbers.
-$\log _ { x } 56 - \log _ { x } 8$

Accepted Answer

A)  $\log _ { x } 48$ 
B)  $\frac { \log _ { x } 56 } { \log _ { x } 8 }$ 
C)  $\log _ { x } 448$ 
D)  $\log _ { x } 7$

Question 18

Evaluate. Round to the nearest thousandth, if necessary.
-In $0.998$

Accepted Answer

A)  $0.001$ 
B)  $- 0.001$ 
C)  $0.002$ 
D)  $- 0.002$

Question 19

Determine the equation of the horizontal asymptote for the graph of this function, and state the domain and range of
this function.
-$$f ( x ) = e ^ { 3 x } - 4$$

Accepted Answer

A)  Horizontal asymptote: $\mathrm { y } = 0$;
Domain: $( - \infty , \infty )$, Range: $( 0 , \infty )$ 
B)  Horizontal asymptote: $\mathrm { y } = - 4$;
Domain: $( - \infty , \infty )$, Range: $( - 4 , \infty )$ 
C)  Horizontal asymptote: $\mathrm { y } = 3$;
Domain: $( - \infty , \infty )$, Range: $( 3 , \infty )$ 
D)  Horizontal asymptote: $\mathrm { y } = 4$;
Domain: $( - \infty , \infty )$, Range: $( 4 , \infty )$

Question 20

Rewrite in logarithmic form.
-$$10 ^ { 5 } = 100,000$$

Accepted Answer

A)  $\log _ { 5 } 10 = 100,000$ 
B)  $\log 5 = 100,000$ 
C)  $\log 100,000 = 5$ 
D)  $\log _ { 5 } 100,000 = 10$

Exam 12: Logarithmic and Exponential Functions

Determine the equation of the horizontal asymptote for the graph of this function, and state the domain and range of this function. - $f ( x ) = \log _ { 5 } ( x + 1 ) + 3$

Rewrite as a single logarithm. Assume all variables represent positive real numbers. - $4 \log _ { 4 } ( 4 x + 2 ) + 3 \log _ { 4 } ( 5 x + 3 )$

Rewrite as a single logarithm using the quotient rule for logarithms. Assume all variables represent positive real numbers. - $\log _ { b } s - \log _ { b } x$

Expand. Assume that all variables represent positive real numbers. - $\log _ { \mathrm { b } } \mathrm { yz } 4$

Solve the problem. -The population growth of an animal species is described by F(t) = 300 + 20 log3 (2t + 1) , where t is measured in months. Find the population of this species in an area 4 month(s) after the species is Introduced.

Evaluate the given function. - $f ( x ) = 2 ^ { x } , f ( 4 )$

Rewrite as the sum of two or more logarithms using the product rule for logarithms. Assume all variables represent positive real numbers. - $\log _ { 4 }$ (xy)

Compute the compound interest. -How long will it take for $5000 to grow to $15,500 at an interest rate of 3.1% if the interest is compounded quarterly? Round the number of years to the nearest hundredth.

Evaluate. Round to the nearest thousandth, if necessary. - $\log 10,000$

Rewrite as a single logarithm. Assume all variables represent positive real numbers. - $\log \sqrt [ 4 ] { x } + \log x ^ { 4 } - \log x ^ { 3 }$

Determine the equation of the horizontal asymptote for the graph of this function, and state the domain and range of this function. - $f ( x ) = 5 ^ { x } + 4$

Evaluate. Round to the nearest thousandth, if necessary. - $\ln \left( e ^ { - 5 } \right)$

Evaluate the given function. - $f ( x ) = 3 ^ { x + 1 } + 3 , f ( 3 )$

Rewrite in logarithmic form. -The sales of a new product (in items per month) can be approximated by $S ( x ) = 300 + 100 \log ( 3 t + 1 )$

Rewrite as a single logarithm using the quotient rule for logarithms. Assume all variables represent positive real numbers. - $\log _ { x } 56 - \log _ { x } 8$

Evaluate. Round to the nearest thousandth, if necessary. -In $0.998$

Determine the equation of the horizontal asymptote for the graph of this function, and state the domain and range of this function. - $f ( x ) = e ^ { 3 x } - 4$

Rewrite in logarithmic form. - $10 ^ { 5 } = 100,000$

Exam 12: Logarithmic and Exponential Functions

Determine the equation of the horizontal asymptote for the graph of this function, and state the domain and range of this function. - f(x) =log⁡5(x+1) +3f ( x ) = \log _ { 5 } ( x + 1 ) + 3f(x) =log5​(x+1) +3

Rewrite as a single logarithm. Assume all variables represent positive real numbers. - 4log⁡4(4x+2) +3log⁡4(5x+3) 4 \log _ { 4 } ( 4 x + 2 ) + 3 \log _ { 4 } ( 5 x + 3 ) 4log4​(4x+2) +3log4​(5x+3)

Rewrite as a single logarithm using the quotient rule for logarithms. Assume all variables represent positive real numbers. - log⁡bs−log⁡bx\log _ { b } s - \log _ { b } xlogb​s−logb​x

Expand. Assume that all variables represent positive real numbers. - log⁡byz4\log _ { \mathrm { b } } \mathrm { yz } 4logb​yz4

Solve the problem. -The population growth of an animal species is described by F(t) = 300 + 20 log3 (2t + 1) , where t is measured in months. Find the population of this species in an area 4 month(s) after the species is Introduced.

Evaluate the given function. - f(x) =2x,f(4) f ( x ) = 2 ^ { x } , f ( 4 ) f(x) =2x,f(4)

Rewrite as the sum of two or more logarithms using the product rule for logarithms. Assume all variables represent positive real numbers. - log⁡4\log _ { 4 }log4​ (xy)

Compute the compound interest. -How long will it take for $5000 to grow to $15,500 at an interest rate of 3.1% if the interest is compounded quarterly? Round the number of years to the nearest hundredth.

Evaluate. Round to the nearest thousandth, if necessary. - log⁡10,000\log 10,000log10,000

Rewrite as a single logarithm. Assume all variables represent positive real numbers. - log⁡x4+log⁡x4−log⁡x3\log \sqrt [ 4 ] { x } + \log x ^ { 4 } - \log x ^ { 3 }log4x​+logx4−logx3

Determine the equation of the horizontal asymptote for the graph of this function, and state the domain and range of this function. - f(x) =5x+4f ( x ) = 5 ^ { x } + 4f(x) =5x+4

Evaluate. Round to the nearest thousandth, if necessary. - ln⁡(e−5) \ln \left( e ^ { - 5 } \right) ln(e−5)

Evaluate the given function. - f(x) =3x+1+3,f(3) f ( x ) = 3 ^ { x + 1 } + 3 , f ( 3 ) f(x) =3x+1+3,f(3)

Rewrite in logarithmic form. -The sales of a new product (in items per month) can be approximated by S(x) =300+100log⁡(3t+1) S ( x ) = 300 + 100 \log ( 3 t + 1 ) S(x) =300+100log(3t+1)

Rewrite as a single logarithm using the quotient rule for logarithms. Assume all variables represent positive real numbers. - log⁡x56−log⁡x8\log _ { x } 56 - \log _ { x } 8logx​56−logx​8

Evaluate. Round to the nearest thousandth, if necessary. -In 0.9980.9980.998

Determine the equation of the horizontal asymptote for the graph of this function, and state the domain and range of this function. - f(x) =e3x−4f ( x ) = e ^ { 3 x } - 4f(x) =e3x−4

Rewrite in logarithmic form. - 105=100,00010 ^ { 5 } = 100,000105=100,000