Question 1

Expand. Assume that all variables represent positive real numbers.
-$\log _ { 19 } \left( \frac { 5 } { s ^ { 2 } r } \right)$

Accepted Answer

A)  $\frac { 1 } { 5 } \log _ { 19 } 3 - 2 \log _ { 19 } s - 2 \log _ { 19 } r$ 
B)  $\log _ { 19 } 3 - \log _ { 19 } s - \log _ { 19 } r$ 
C)  $\frac { 1 } { 5 } \log _ { 19 } 3 - 2 \log _ { 19 } s - \log _ { 19 } \mathrm { r }$ 
D)  $5 \log _ { 19 } 3 - 2 \log _ { 19 } s - \log _ { 19 } 5$ 
A)  $\frac { 1 } { 5 } \log _ { 19 } 3 - 2 \log _ { 19 } s - 2 \log _ { 19 } r$ 
B)  $\log _ { 19 } 3 - \log _ { 19 } s - \log _ { 19 } r$ 
C)  $\frac { 1 } { 5 } \log _ { 19 } 3 - 2 \log _ { 19 } s - \log _ { 19 } \mathrm { r }$ 
D)  $5 \log _ { 19 } 3 - 2 \log _ { 19 } s - \log _ { 19 } 5$

Question 2

Rewrite as a single logarithm using the quotient rule for logarithms. Assume all variables represent positive real
numbers.
-$$\log _ { 3 } 8 - \log _ { 3 } 12$$

Accepted Answer

A)  $\log _ { 6 } \frac { 2 } { 3 }$ 
B)  $\log _ { 3 } \frac { 3 } { 2 }$ 
C)  $\log _ { 3 } \frac { 2 } { 3 }$ 
D)  $\log _ { 3 } - 4$ 
A)  $\log _ { 6 } \frac { 2 } { 3 }$ 
B)  $\log _ { 3 } \frac { 3 } { 2 }$ 
C)  $\log _ { 3 } \frac { 2 } { 3 }$ 
D)  $\log _ { 3 } - 4$

Question 3

Solve.
-There are currently 51 million cars in a certain country, increasing exponentially by 4.4% annually. How many years will it take for this country to have 60 million cars? Round to the nearest year.

Accepted Answer

A)  3 yr 
B)  4 yr 
C)  2 yr 
D)  50 yr 
A)  3 yr 
B)  4 yr 
C)  2 yr 
D)  50 yr

Question 4

Rewrite in terms of two or more logarithms using the quotient and product rules for logarithms. Assume all variables
represent positive real numbers.
-$\log 17 \left( \frac { 5 \mathrm {~m} } { \mathrm { y } } \right)$

Accepted Answer

A)  $\frac { \log _ { 17 } 5 + \log _ { 17 } \mathrm {~m} } { \log 17 \mathrm { y } }$ 
B)  $\log 175 - \log 17 m - \log 17 \mathrm { y }$ 
C)  $( \log 175 ) ( \log 17 \mathrm {~m} ) - \log 17 \mathrm { y }$ 
D)  $\log 175 + \log 17 m - \log 17 \mathrm { y }$ 
A)  $\frac { \log _ { 17 } 5 + \log _ { 17 } \mathrm {~m} } { \log 17 \mathrm { y } }$ 
B)  $\log 175 - \log 17 m - \log 17 \mathrm { y }$ 
C)  $( \log 175 ) ( \log 17 \mathrm {~m} ) - \log 17 \mathrm { y }$ 
D)  $\log 175 + \log 17 m - \log 17 \mathrm { y }$

Question 5

Solve the problem.
-A loan of $\$ 8000$ is made at $5 \%$ interest, compounded annually. After t years, the amount due, $A$, is given by the function $\mathrm { A } ( \mathrm { t } ) = 8000 ( 1.05 ) ^ { \mathrm { t } } \text {. }$ Find the doubling time. Round your answer to the nearest tenth.

Accepted Answer

A)  $28.4 \mathrm { yr }$ 
B)  $22.5 \mathrm { yr }$ 
C)  $14.2 \mathrm { yr }$ 
D)  $41.0 \mathrm { yr }$ 
A)  $28.4 \mathrm { yr }$ 
B)  $22.5 \mathrm { yr }$ 
C)  $14.2 \mathrm { yr }$ 
D)  $41.0 \mathrm { yr }$

Question 6

Find the missing number. Round to the nearest hundredth if necessary.
-$2 ^ { ? } = 8$

Accepted Answer

A)  3 
B)  2 
C)  $- 3$ 
D)  4 
A)  3 
B)  2 
C)  $- 3$ 
D)  4

Question 7

Rewrite in logarithmic form.
-The space in a landfill decreases with time as given by the function F(t) = 320 - 40 log5 (4t + 1), where t is measured in years. How much space is left when t = 31?

Accepted Answer

A)  200 
B)  440 
C)  240 
D)  110 
A)  200 
B)  440 
C)  240 
D)  110

Question 8

Evaluate the given function.
-$$f ( x ) = 4 ^ { x } , f ( - 3 )$$

Accepted Answer

A)  $\frac { 1 } { 12 }$ 
B)  $\frac { 1 } { 64 }$ 
C)  $- \frac { 4 } { 3 }$ 
D)  12 
A)  $\frac { 1 } { 12 }$ 
B)  $\frac { 1 } { 64 }$ 
C)  $- \frac { 4 } { 3 }$ 
D)  12

Question 9

Evaluate using the change-of-base formula. Round to four decimal places.
-$\log _ { 2.4 } 200$

Accepted Answer

A)  $0.1652$ 
B)  $83.3333$ 
C)  $2.3010$ 
D)  $6.0520$ 
A)  $0.1652$ 
B)  $83.3333$ 
C)  $2.3010$ 
D)  $6.0520$

Question 10

Rewrite using the power rule. Assume all variables represent positive real numbers.
-$\log _ { 5 } y ^ { 7 }$

Accepted Answer

A)  $35 \log y$ 
B)  $\log _ { 5 } 7 y$ 
C)  $7 \log 5 y$ 
D)  $7 \log _ { 5 } y$ 
A)  $35 \log y$ 
B)  $\log _ { 5 } 7 y$ 
C)  $7 \log 5 y$ 
D)  $7 \log _ { 5 } y$

Question 11

Solve the problem.
-A college loan of $\$ 26,000$ is made at $4 \%$ interest, compounded annually. After t years, the amount due, $A$, is given by the function $A ( t ) = 26,000 ( 1.04 ) ^ { t } \text {. }$ After what amount of time will the amount reach $\$ 41,000$ ? Round your answer to the nearest tenth.

Accepted Answer

A)  $0.1 \mathrm { yr }$ 
B)  $11.6 \mathrm { yr }$ 
C)  $70.3 \mathrm { yr }$ 
D)  $0.4 \mathrm { yr }$ 
A)  $0.1 \mathrm { yr }$ 
B)  $11.6 \mathrm { yr }$ 
C)  $70.3 \mathrm { yr }$ 
D)  $0.4 \mathrm { yr }$

Question 12

Rewrite using the power rule. Assume all variables represent positive real numbers.
-$\log _ { b } y ^ { 9 }$

Accepted Answer

A)  $b \log _ { 9 } y$ 
B)  $9 \log _ { b } y$ 
C)  $9 \log _ { b } \mathrm { y } ^ { 9 }$ 
D)  b $\log _ { 90 } \mathrm { y } ^ { 9 }$ 
A)  $b \log _ { 9 } y$ 
B)  $9 \log _ { b } y$ 
C)  $9 \log _ { b } \mathrm { y } ^ { 9 }$ 
D)  b $\log _ { 90 } \mathrm { y } ^ { 9 }$

Question 13

Evaluate the given function.
-$f ( x ) = \left( \frac { 1 } { 5 } \right) ^ { x }$
$f ( 2 )$

Accepted Answer

A)  25 
B)  $\frac { 1 } { 10 }$ 
C)  $\frac { 1 } { 32 }$ 
D)  $\frac { 1 } { 25 }$ 
A)  25 
B)  $\frac { 1 } { 10 }$ 
C)  $\frac { 1 } { 32 }$ 
D)  $\frac { 1 } { 25 }$

Question 14

Suppose for some base b > 0 (b ≠ 1) that logb 2 = A, logb 3 = B, logb 5 = C, and logb 7 = D. Express the given logarithms
in terms of A, B, C, or D.
-$\log _ { \mathrm { b } } 14$

Accepted Answer

A)  $B + C$ 
B)  $C + D$ 
C)  $A + B$ 
D)  $A + D$ 
A)  $B + C$ 
B)  $C + D$ 
C)  $A + B$ 
D)  $A + D$

Question 15

Simplify.
-$\mathrm { e } ^ { \ln 0.357 }$

Accepted Answer

A)  $- 0.357$ 
B)  $\log 0.357$ 
C)  $\ln - 0.357$ 
D)  $0.357$ 
A)  $- 0.357$ 
B)  $\log 0.357$ 
C)  $\ln - 0.357$ 
D)  $0.357$

Question 16

Determine the equation of the horizontal asymptote for the graph of this function, and state the domain and range of
this function.
-$$f ( x ) = 3 ^ { x - 2 }$$

Accepted Answer

A)  Horizontal asymptote: $y = 3$;
Domain: $( - \infty , \infty )$, Range: $( 3 , \infty )$ 
B)  Horizontal asymptote: $\mathrm { y } = 0$;
Domain: $( - \infty , \infty )$, Range: $( 0 , \infty )$ 
C)  Horizontal asymptote: $y = 2$;
Domain: $( - \infty , \infty )$, Range: $( 2 , \infty )$ 
D)  Horizontal asymptote: $y = - 2$;
Domain: $( - \infty , \infty )$, Range: $( - 2 , \infty )$ 
A)  Horizontal asymptote: $y = 3$;
Domain: $( - \infty , \infty )$, Range: $( 3 , \infty )$ 
B)  Horizontal asymptote: $\mathrm { y } = 0$;
Domain: $( - \infty , \infty )$, Range: $( 0 , \infty )$ 
C)  Horizontal asymptote: $y = 2$;
Domain: $( - \infty , \infty )$, Range: $( 2 , \infty )$ 
D)  Horizontal asymptote: $y = - 2$;
Domain: $( - \infty , \infty )$, Range: $( - 2 , \infty )$

Question 17

Rewrite in terms of two or more logarithms using the quotient and product rules for logarithms. Assume all variables
represent positive real numbers.
-$\log _ { w } \left( \frac { 11 x } { 5 } \right)$

Accepted Answer

A)  $\log _ { \mathrm { W } } 11 + \log _ { \mathrm { W } } \mathrm { x } - \log _ { \mathrm { W } } 5$ 
B)  $\log _ { \mathrm { W } } 6 \mathrm { x }$ 
C)  $\log _ { W } 11 + \log _ { W } x + \log _ { W } 5$ 
D)  $\log _ { W } 11 \mathrm { x } - \log _ { \mathrm { W } } 5$ 
A)  $\log _ { \mathrm { W } } 11 + \log _ { \mathrm { W } } \mathrm { x } - \log _ { \mathrm { W } } 5$ 
B)  $\log _ { \mathrm { W } } 6 \mathrm { x }$ 
C)  $\log _ { W } 11 + \log _ { W } x + \log _ { W } 5$ 
D)  $\log _ { W } 11 \mathrm { x } - \log _ { \mathrm { W } } 5$

Question 18

Solve the problem.
-A certain country's population $\mathrm { P } ( \mathrm { t } )$, in millions, t years after 1980 can be approximated by $\mathrm { P } ( \mathrm { t } ) = 2.495 ( 1.018 ) ^ { \mathrm { t } } \text {. }$ Find the doubling time. Round your answer to the nearest tenth.

Accepted Answer

A)  $61.6 \mathrm { yr }$ 
B)  $38.9 \mathrm { yr }$ 
C)  $77.7 \mathrm { yr }$ 
D)  $51.2 \mathrm { yr }$ 
A)  $61.6 \mathrm { yr }$ 
B)  $38.9 \mathrm { yr }$ 
C)  $77.7 \mathrm { yr }$ 
D)  $51.2 \mathrm { yr }$

Question 19

Rewrite as a single logarithm using the product rule for logarithms. Assume all variables represent positive real
numbers.
-$\log _ { 4 } 9 + \log _ { 4 } 6$

Accepted Answer

A)  $\log _ { 4 } 54$ 
B)  $\log _ { 8 } 15$ 
C)  $\log _ { 8 } 54$ 
D)  $\log _ { 4 } 15$ 
A)  $\log _ { 4 } 54$ 
B)  $\log _ { 8 } 15$ 
C)  $\log _ { 8 } 54$ 
D)  $\log _ { 4 } 15$

Question 20

Rewrite using the power rule. Assume all variables represent positive real numbers.
-$\log _ { 4 } 4 ^ { - 5 }$

Accepted Answer

A)  $- 5$ 
B)  $- 20$ 
C)  1 
D)  4 
A)  $- 5$ 
B)  $- 20$ 
C)  1 
D)  4

Expand. Assume that all variables represent positive real numbers. - $\log _ { 19 } \left( \frac { 5 } { s ^ { 2 } r } \right)$

Rewrite as a single logarithm using the quotient rule for logarithms. Assume all variables represent positive real numbers. - $\log _ { 3 } 8 - \log _ { 3 } 12$

Solve. -There are currently 51 million cars in a certain country, increasing exponentially by 4.4% annually. How many years will it take for this country to have 60 million cars? Round to the nearest year.

Rewrite in terms of two or more logarithms using the quotient and product rules for logarithms. Assume all variables represent positive real numbers. - $\log 17 \left( \frac { 5 \mathrm {~m} } { \mathrm { y } } \right)$

Solve the problem. -A loan of $\$ 8000$ is made at $5 \%$ interest, compounded annually. After t years, the amount due, $A$ , is given by the function $\mathrm { A } ( \mathrm { t } ) = 8000 ( 1.05 ) ^ { \mathrm { t } } \text {. }$ Find the doubling time. Round your answer to the nearest tenth.

Find the missing number. Round to the nearest hundredth if necessary. - $2 ^ { ? } = 8$

Rewrite in logarithmic form. -The space in a landfill decreases with time as given by the function F(t) = 320 - 40 log5 (4t + 1), where t is measured in years. How much space is left when t = 31?

Evaluate the given function. - $f ( x ) = 4 ^ { x } , f ( - 3 )$

Evaluate using the change-of-base formula. Round to four decimal places. - $\log _ { 2.4 } 200$

Rewrite using the power rule. Assume all variables represent positive real numbers. - $\log _ { 5 } y ^ { 7 }$

Rewrite using the power rule. Assume all variables represent positive real numbers. - $\log _ { b } y ^ { 9 }$

Evaluate the given function. - $f ( x ) = \left( \frac { 1 } { 5 } \right) ^ { x }$ $f ( 2 )$

Suppose for some base b > 0 (b ≠ 1) that logb 2 = A, logb 3 = B, logb 5 = C, and logb 7 = D. Express the given logarithms in terms of A, B, C, or D. - $\log _ { \mathrm { b } } 14$

Simplify. - $\mathrm { e } ^ { \ln 0.357 }$

Determine the equation of the horizontal asymptote for the graph of this function, and state the domain and range of this function. - $f ( x ) = 3 ^ { x - 2 }$

Rewrite in terms of two or more logarithms using the quotient and product rules for logarithms. Assume all variables represent positive real numbers. - $\log _ { w } \left( \frac { 11 x } { 5 } \right)$

Solve the problem. -A certain country's population $\mathrm { P } ( \mathrm { t } )$ , in millions, t years after 1980 can be approximated by $\mathrm { P } ( \mathrm { t } ) = 2.495 ( 1.018 ) ^ { \mathrm { t } } \text {. }$ Find the doubling time. Round your answer to the nearest tenth.

Rewrite as a single logarithm using the product rule for logarithms. Assume all variables represent positive real numbers. - $\log _ { 4 } 9 + \log _ { 4 } 6$

Rewrite using the power rule. Assume all variables represent positive real numbers. - $\log _ { 4 } 4 ^ { - 5 }$

Review of Real Numbers

Linear Equations

Graphing Linear Equations

Systems of Equations

Exponents and Polynomials

Factoring and Quadratic Equations

Rational Expressions and Equations

A Transition

Radical Expressions and Equations

Quadratic Equations

Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 12: Logarithmic and Exponential Functions

Expand. Assume that all variables represent positive real numbers. - log⁡19(5s2r)\log _ { 19 } \left( \frac { 5 } { s ^ { 2 } r } \right)log19​(s2r5​)

Rewrite as a single logarithm using the quotient rule for logarithms. Assume all variables represent positive real numbers. - log⁡38−log⁡312\log _ { 3 } 8 - \log _ { 3 } 12log3​8−log3​12