Question 1

Write an equation for the graph given. The graph represents an logarithmic function f with base 2 or 3, translated and/or
reflected.
-

Accepted Answer

A)  $\log _ { 2 } ( x - 1 ) - 2$ 
B)  $\log _ { 2 } ( x + 1 ) - 2$ 
C)  $\log _ { 2 } ( x + 1 ) + 2$ 
D)  $\log _ { 2 } ( x - 1 ) + 2$ 
A)  $\log _ { 2 } ( x - 1 ) - 2$ 
B)  $\log _ { 2 } ( x + 1 ) - 2$ 
C)  $\log _ { 2 } ( x + 1 ) + 2$ 
D)  $\log _ { 2 } ( x - 1 ) + 2$

Question 2

Solve the equation.
-$$a ^ { 3 / 4 } = 125$$

Accepted Answer

A)  $\{ 625 \}$ 
B)  $\{ - 5,5 \}$ 
C)  $\{ - 625,625 \}$ 
D)  $\{ 5 \}$ 
A)  $\{ 625 \}$ 
B)  $\{ - 5,5 \}$ 
C)  $\{ - 625,625 \}$ 
D)  $\{ 5 \}$

Question 3

Determine whether or not the function is one-to-one.
-

Accepted Answer

A)  No 
B)  Yes 
A)  No 
B)  Yes

Question 4

Determine whether the statement is true or false.
-$f ( x ) = x ^ { n }$ where n is an odd integer, has an inverse.

Accepted Answer

A) True 
 B)False

Question 5

Write the word or phrase that best completes each statement or answers the question.
-Explain why a $\log _ { a } 5 = 5$

Accepted Answer

The answer of Write the word or phrase that best...

Question 6

Write the expression as a single logarithm with coefficient 1. Assume all variables represent positive real numbers with $$a \neq 1 \text { and } b \neq 1$$
-$6 \log _ { a } t - \log _ { a } s$

Accepted Answer

A)  $\log _ { a } t ^ { 6 } \div \log _ { a } s$ 
B)  $\log _ { a } \left( \frac { t ^ { 6 } } { s } \right)$ 
C)  $\log _ { a } \left( t ^ { 6 } - s \right)$ 
D)  $\log _ { a } \left( \frac { 6 t } { s } \right)$ 
A)  $\log _ { a } t ^ { 6 } \div \log _ { a } s$ 
B)  $\log _ { a } \left( \frac { t ^ { 6 } } { s } \right)$ 
C)  $\log _ { a } \left( t ^ { 6 } - s \right)$ 
D)  $\log _ { a } \left( \frac { 6 t } { s } \right)$

Question 7

Solve the following graphically. If necessary, round answers to the nearest thousandth.
-$$\mathrm { e } ^ { \mathrm { x } } + \ln 3 = 2 \mathrm { e } ^ { \mathrm { x } }$$

Accepted Answer

A)  $\{ 0.188 \}$ 
B)  $\{ - 1.005 \}$ 
C)  $\{ 0.094 \}$ 
D)  $\{ 1.099 \}$ 
A)  $\{ 0.188 \}$ 
B)  $\{ - 1.005 \}$ 
C)  $\{ 0.094 \}$ 
D)  $\{ 1.099 \}$

Question 8

Find the domain and range of the inverse of the given function.
-$$f ( x ) = \sqrt [ 3 ] { 4 x - 1 }$$

Accepted Answer

A)  Domain: $[ 0 , \infty )$; range: all real numbers 
B)  Domain: all real numbers; range: $[ 0 , \infty )$ 
C)  Domain and range: all real numbers 
D)  Domain: $[ 1 , \infty )$; range: $[ 0 , \infty )$ 
A)  Domain: $[ 0 , \infty )$; range: all real numbers 
B)  Domain: all real numbers; range: $[ 0 , \infty )$ 
C)  Domain and range: all real numbers 
D)  Domain: $[ 1 , \infty )$; range: $[ 0 , \infty )$

Question 9

Choose the one alternative that best completes the statement or answers the question.
-How long will it take for $\$ 6100$ to grow to $\$ 26,700$ at an interest rate of $4.6 \%$ if the interest is compounded continuously? Round the number of years to the nearest hundredth.

Accepted Answer

A)  $3.21 \mathrm { yr }$ 
B)  $1.01 \mathrm { yr }$ 
C)  $32.10 \mathrm { yr }$ 
D)  $3209.51 \mathrm { yr }$ 
A)  $3.21 \mathrm { yr }$ 
B)  $1.01 \mathrm { yr }$ 
C)  $32.10 \mathrm { yr }$ 
D)  $3209.51 \mathrm { yr }$

Question 10

Use properties of logarithms to evaluate the expression.
-If $\mathrm { f } ( \mathrm { x } ) = 14 ^ { \mathrm { x } }$, find $\mathrm { f } \left[ \log _ { 14 } ( \ln 14 ) \right]$

Accepted Answer

A)  $14 ^ { \ln 14 }$ 
B)  $\log _ { 14 } 14$ 
C)  0 
D)  $\ln 14$ 
A)  $14 ^ { \ln 14 }$ 
B)  $\log _ { 14 } 14$ 
C)  0 
D)  $\ln 14$

Question 11

If the function is one-to-one, find its inverse. If not, write "not one-to-one."
-$$f ( x ) = x ^ { 3 } + 4$$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x + 4 }$ 
B)  $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x } - 4$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 3 ] { \mathrm { x } - 4 }$ 
D)  not a one-to-one 
A)  $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x + 4 }$ 
B)  $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x } - 4$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 3 ] { \mathrm { x } - 4 }$ 
D)  not a one-to-one

Question 12

Solve the equation. Round to the nearest thousandth.
-$114 ( 1.93 ) ^ { x / 5 } = 228$

Accepted Answer

A)  $\{ 6.491 \}$ 
B)  $\{ 4.743 \}$ 
C)  $\{ 5.271 \}$ 
D)  $\{ 4.051 \}$ 
A)  $\{ 6.491 \}$ 
B)  $\{ 4.743 \}$ 
C)  $\{ 5.271 \}$ 
D)  $\{ 4.051 \}$

Question 13

Use the graph of f to sketch a graph of the inverse of f using a dashed curve.
-

Accepted Answer

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

Question 14

Find the present value of the future value.
-The sales of a mature product (one which has passed its peak) will decline according to the function $$S ( t ) = S _ { 0 } e ^ { - a t }$$ , where t is time in years since the peak sales. Find the sales of a product 24 years after its peak sales if a = 0.23 and $$\mathrm { S } _ { 0 } = 35,000$$

Accepted Answer

A)  140 units 
B)  10,996,672 units 
C)  70 units 
D)  44,051 units 
A)  140 units 
B)  10,996,672 units 
C)  70 units 
D)  44,051 units

Question 15

Use the properties of logarithms to rewrite the expression. Simplify the result if possible. Assume all variables represent
positive real numbers.
-$$\log _ { 11 } \left( \frac { 13 \mathrm {~m} } { \mathrm { y } } \right)$$

Accepted Answer

A)  $\left( \log _ { 11 } 13 \right) ( \log 11 \mathrm {~m} ) - \log 11 \mathrm { y }$ 
B)  $\log 1113 - \log 11 m - \log 11 y$ 
C)  $\log 1113 + \log 11 m - \log 11 y$ 
D)  $\frac { \log 1113 + \log 11 \mathrm {~m} } { \log 11 \mathrm { y } }$ 
A)  $\left( \log _ { 11 } 13 \right) ( \log 11 \mathrm {~m} ) - \log 11 \mathrm { y }$ 
B)  $\log 1113 - \log 11 m - \log 11 y$ 
C)  $\log 1113 + \log 11 m - \log 11 y$ 
D)  $\frac { \log 1113 + \log 11 \mathrm {~m} } { \log 11 \mathrm { y } }$

Question 16

Solve the following graphically. If necessary, round answers to the nearest thousandth.
-$$\mathrm { e } ^ { \mathrm { x } + 2 } = \frac { 1 } { x + 4 }$$

Accepted Answer

A)  $\{ - 5.5777 , - 2.4284 \}$ 
B)  $\varnothing$ 
C)  $\{ - 2.443 \}$ 
D)  $\{ - 4.000 , - 2.443 \}$ 
A)  $\{ - 5.5777 , - 2.4284 \}$ 
B)  $\varnothing$ 
C)  $\{ - 2.443 \}$ 
D)  $\{ - 4.000 , - 2.443 \}$

Question 17

Use the graph of f to sketch a graph of the inverse of f using a dashed curve.
-

Accepted Answer

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

Question 18

rite the word or phrase that best completes each statement or answers the question.
-Write the algebraic equation which can be used to find the exact solution of $$\log _ { 3 } ( x - 8 ) + \log _ { 3 } ( x + 2 ) = 4$$

Accepted Answer

The answer of rite the word or phrase that best...

Question 19

Use the change of base rule to find the logarithm to four decimal places.
-$$\log _ { 9 } 0.912$$

Accepted Answer

A)  -23.8530 
B)  -0.0419 
C)  -0.0400 
D)  9.8684 
A)  -23.8530 
B)  -0.0419 
C)  -0.0400 
D)  9.8684

Question 20

Solve the problem.
-$$\mathrm { p } ( \mathrm { t } ) = 3156 \mathrm { e } ^ { 0.006 \mathrm { t } }$$ , where t is the number of years. According to this formula, in how many years will the population reach 4734?
Round to the nearest tenth of a year.

Accepted Answer

A)  33.8 yr 
B)  67.6 yr 
C)  50.7 yr 
D)  135.2 yr 
A)  33.8 yr 
B)  67.6 yr 
C)  50.7 yr 
D)  135.2 yr

Write an equation for the graph given. The graph represents an logarithmic function f with base 2 or 3, translated and/or reflected. -

Solve the equation. - $a ^ { 3 / 4 } = 125$

Determine whether or not the function is one-to-one. -

Determine whether the statement is true or false. - $f ( x ) = x ^ { n }$ where n is an odd integer, has an inverse.

Write the word or phrase that best completes each statement or answers the question. -Explain why a $\log _ { a } 5 = 5$

Write the expression as a single logarithm with coefficient 1. Assume all variables represent positive real numbers with $a \neq 1 \text { and } b \neq 1$ - $6 \log _ { a } t - \log _ { a } s$

Solve the following graphically. If necessary, round answers to the nearest thousandth. - $\mathrm { e } ^ { \mathrm { x } } + \ln 3 = 2 \mathrm { e } ^ { \mathrm { x } }$

Find the domain and range of the inverse of the given function. - $f ( x ) = \sqrt [ 3 ] { 4 x - 1 }$

Choose the one alternative that best completes the statement or answers the question. -How long will it take for $\$ 6100$ to grow to $\$ 26,700$ at an interest rate of $4.6 \%$ if the interest is compounded continuously? Round the number of years to the nearest hundredth.

Use properties of logarithms to evaluate the expression. -If $\mathrm { f } ( \mathrm { x } ) = 14 ^ { \mathrm { x } }$ , find $\mathrm { f } \left[ \log _ { 14 } ( \ln 14 ) \right]$

If the function is one-to-one, find its inverse. If not, write "not one-to-one." - $f ( x ) = x ^ { 3 } + 4$

Solve the equation. Round to the nearest thousandth. - $114 ( 1.93 ) ^ { x / 5 } = 228$

Use the graph of f to sketch a graph of the inverse of f using a dashed curve. -

Use the properties of logarithms to rewrite the expression. Simplify the result if possible. Assume all variables represent positive real numbers. - $\log _ { 11 } \left( \frac { 13 \mathrm {~m} } { \mathrm { y } } \right)$

Solve the following graphically. If necessary, round answers to the nearest thousandth. - $\mathrm { e } ^ { \mathrm { x } + 2 } = \frac { 1 } { x + 4 }$

Use the graph of f to sketch a graph of the inverse of f using a dashed curve. -

rite the word or phrase that best completes each statement or answers the question. -Write the algebraic equation which can be used to find the exact solution of $\log _ { 3 } ( x - 8 ) + \log _ { 3 } ( x + 2 ) = 4$

Use the change of base rule to find the logarithm to four decimal places. - $\log _ { 9 } 0.912$

Solve the problem. - $\mathrm { p } ( \mathrm { t } ) = 3156 \mathrm { e } ^ { 0.006 \mathrm { t } }$ , where t is the number of years. According to this formula, in how many years will the population reach 4734? Round to the nearest tenth of a year.

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Filters

Exam 5: Inverse, Exponential, and Logarithmic Functions

Write an equation for the graph given. The graph represents an logarithmic function f with base 2 or 3, translated and/or reflected. -

Solve the equation. - a3/4=125a ^ { 3 / 4 } = 125a3/4=125

Determine whether or not the function is one-to-one. -

Determine whether the statement is true or false. - f(x)=xnf ( x ) = x ^ { n }f(x)=xn where n is an odd integer, has an inverse.

Write the word or phrase that best completes each statement or answers the question. -Explain why a log⁡a5=5\log _ { a } 5 = 5loga​5=5

Write the expression as a single logarithm with coefficient 1. Assume all variables represent positive real numbers with a≠1 and b≠1a \neq 1 \text { and } b \neq 1a=1 and b=1 - 6log⁡at−log⁡as6 \log _ { a } t - \log _ { a } s6loga​t−loga​s

Solve the following graphically. If necessary, round answers to the nearest thousandth. - ex+ln⁡3=2ex\mathrm { e } ^ { \mathrm { x } } + \ln 3 = 2 \mathrm { e } ^ { \mathrm { x } }ex+ln3=2ex

Find the domain and range of the inverse of the given function. - f(x)=4x−13f ( x ) = \sqrt [ 3 ] { 4 x - 1 }f(x)=34x−1​

Choose the one alternative that best completes the statement or answers the question. -How long will it take for $6100\$ 6100$6100 to grow to $26,700\$ 26,700$26,700 at an interest rate of 4.6%4.6 \%4.6% if the interest is compounded continuously? Round the number of years to the nearest hundredth.

Use properties of logarithms to evaluate the expression. -If f(x)=14x\mathrm { f } ( \mathrm { x } ) = 14 ^ { \mathrm { x } }f(x)=14x , find f[log⁡14(ln⁡14)]\mathrm { f } \left[ \log _ { 14 } ( \ln 14 ) \right]f[log14​(ln14)]

If the function is one-to-one, find its inverse. If not, write "not one-to-one." - f(x)=x3+4f ( x ) = x ^ { 3 } + 4f(x)=x3+4

Solve the equation. Round to the nearest thousandth. - 114(1.93)x/5=228114 ( 1.93 ) ^ { x / 5 } = 228114(1.93)x/5=228

Use the graph of f to sketch a graph of the inverse of f using a dashed curve. -

Use the properties of logarithms to rewrite the expression. Simplify the result if possible. Assume all variables represent positive real numbers. - log⁡11(13 my)\log _ { 11 } \left( \frac { 13 \mathrm {~m} } { \mathrm { y } } \right)log11​(y13 m​)

Solve the following graphically. If necessary, round answers to the nearest thousandth. - ex+2=1x+4\mathrm { e } ^ { \mathrm { x } + 2 } = \frac { 1 } { x + 4 }ex+2=x+41​

Use the graph of f to sketch a graph of the inverse of f using a dashed curve. -

rite the word or phrase that best completes each statement or answers the question. -Write the algebraic equation which can be used to find the exact solution of log⁡3(x−8)+log⁡3(x+2)=4\log _ { 3 } ( x - 8 ) + \log _ { 3 } ( x + 2 ) = 4log3​(x−8)+log3​(x+2)=4

Use the change of base rule to find the logarithm to four decimal places. - log⁡90.912\log _ { 9 } 0.912log9​0.912

Solve the problem. - p(t)=3156e0.006t\mathrm { p } ( \mathrm { t } ) = 3156 \mathrm { e } ^ { 0.006 \mathrm { t } }p(t)=3156e0.006t , where t is the number of years. According to this formula, in how many years will the population reach 4734? Round to the nearest tenth of a year.

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Filters

Solve the equation. - $a ^ { 3 / 4 } = 125$

Determine whether the statement is true or false. - $f ( x ) = x ^ { n }$ where n is an odd integer, has an inverse.

Write the word or phrase that best completes each statement or answers the question. -Explain why a $\log _ { a } 5 = 5$

Write the expression as a single logarithm with coefficient 1. Assume all variables represent positive real numbers with $a \neq 1 \text { and } b \neq 1$ - $6 \log _ { a } t - \log _ { a } s$

Solve the following graphically. If necessary, round answers to the nearest thousandth. - $\mathrm { e } ^ { \mathrm { x } } + \ln 3 = 2 \mathrm { e } ^ { \mathrm { x } }$

Find the domain and range of the inverse of the given function. - $f ( x ) = \sqrt [ 3 ] { 4 x - 1 }$

Choose the one alternative that best completes the statement or answers the question. -How long will it take for $\$ 6100$ to grow to $\$ 26,700$ at an interest rate of $4.6 \%$ if the interest is compounded continuously? Round the number of years to the nearest hundredth.

Use properties of logarithms to evaluate the expression. -If $\mathrm { f } ( \mathrm { x } ) = 14 ^ { \mathrm { x } }$ , find $\mathrm { f } \left[ \log _ { 14 } ( \ln 14 ) \right]$

If the function is one-to-one, find its inverse. If not, write "not one-to-one." - $f ( x ) = x ^ { 3 } + 4$

Solve the equation. Round to the nearest thousandth. - $114 ( 1.93 ) ^ { x / 5 } = 228$

Use the properties of logarithms to rewrite the expression. Simplify the result if possible. Assume all variables represent positive real numbers. - $\log _ { 11 } \left( \frac { 13 \mathrm {~m} } { \mathrm { y } } \right)$

Solve the following graphically. If necessary, round answers to the nearest thousandth. - $\mathrm { e } ^ { \mathrm { x } + 2 } = \frac { 1 } { x + 4 }$

rite the word or phrase that best completes each statement or answers the question. -Write the algebraic equation which can be used to find the exact solution of $\log _ { 3 } ( x - 8 ) + \log _ { 3 } ( x + 2 ) = 4$

Use the change of base rule to find the logarithm to four decimal places. - $\log _ { 9 } 0.912$

Solve the problem. - $\mathrm { p } ( \mathrm { t } ) = 3156 \mathrm { e } ^ { 0.006 \mathrm { t } }$ , where t is the number of years. According to this formula, in how many years will the population reach 4734? Round to the nearest tenth of a year.