Question 1

Write the equation in its equivalent exponential form.
-$$\log _ { 4 } 64 = 3$$

Accepted Answer

A)  $4 ^ { 64 } = 3$ 
B)  $3 ^ { 4 } = 64$ 
C)  $64 ^ { 3 } = 4$ 
D)  $4 ^ { 3 } = 64$ 
A)  $4 ^ { 64 } = 3$ 
B)  $3 ^ { 4 } = 64$ 
C)  $64 ^ { 3 } = 4$ 
D)  $4 ^ { 3 } = 64$

Question 2

The graph of an exponential function is given. Select the function for the graph from the functions listed.
-

Accepted Answer

A)  $f ( x ) = 4 ^ { x } + 2$ 
B)  $f ( x ) = 4 ^ { x }$ 
C)  $f ( x ) = 4 ^ { x } - 2$ 
D)  $f ( x ) = 4 ^ { x - 2 }$ 
A)  $f ( x ) = 4 ^ { x } + 2$ 
B)  $f ( x ) = 4 ^ { x }$ 
C)  $f ( x ) = 4 ^ { x } - 2$ 
D)  $f ( x ) = 4 ^ { x - 2 }$

Question 3

Use the compound interest formulas A $$A = P \left( 1 + \frac { r } { n } \right) ^ { n t }$$ and A = Pert to solve.
-Find the accumulated value of an investment of $17,000 at 6.5% compounded semiannually for 6 years.

Accepted Answer

A)  $23,630.00 
B)  $24,805.42 
C)  $24,953.40 
D)  $20,596.30 
A)  $23,630.00 
B)  $24,805.42 
C)  $24,953.40 
D)  $20,596.30

Question 4

Approximate the number using a calculator. Round the answer to three decimal places.
-$$\mathrm { e } ^ { - 0.5 }$$

Accepted Answer

A)  -0.607 
B)  0.607 
C)  -1.359 
D)  0.907 
A)  -0.607 
B)  0.607 
C)  -1.359 
D)  0.907

Question 5

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
-$\ln \sqrt [ 3 ] { e x }$

Accepted Answer

A)  $\frac { 1 } { 3 } + \ln x$ 
B)  $\frac { 1 } { 3 } \ln \mathrm { e } + \frac { 1 } { 3 } \ln \mathrm { x }$ 
C)  $\frac { 1 } { 3 } + \frac { 1 } { 3 } \ln x$ 
D)  $\frac { 1 } { 3 } \ln ( e x )$ 
A)  $\frac { 1 } { 3 } + \ln x$ 
B)  $\frac { 1 } { 3 } \ln \mathrm { e } + \frac { 1 } { 3 } \ln \mathrm { x }$ 
C)  $\frac { 1 } { 3 } + \frac { 1 } { 3 } \ln x$ 
D)  $\frac { 1 } { 3 } \ln ( e x )$

Question 6

The graph of an exponential function is given. Select the function for the graph from the functions listed.
-

Accepted Answer

A)  $f ( x ) = 5 ^ { x }$ 
B)  $f ( x ) = - 5 ^ { - x }$ 
C)  $f ( x ) = 5 ^ { - x }$ 
D)  $f ( x ) = - 5 ^ { x }$ 
A)  $f ( x ) = 5 ^ { x }$ 
B)  $f ( x ) = - 5 ^ { - x }$ 
C)  $f ( x ) = 5 ^ { - x }$ 
D)  $f ( x ) = - 5 ^ { x }$

Question 7

Solve the problem.
-The growth in the mouse population at a certain county dump can be modeled by the exponential function $$\mathrm { A } ( \mathrm { t } ) = 224 \mathrm { e } ^ { 0.019 \mathrm { t } }$$ where t is the number of months since the population was first recorded. Estimate the population after 28 months.

Accepted Answer

A)  389 mice 
B)  381 mice 
C)  191 mice 
D)  228 mice 
A)  389 mice 
B)  381 mice 
C)  191 mice 
D)  228 mice

Question 8

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
-$\log _ { 8 } ( 8 x )$

Accepted Answer

A)  $1 + \log _ { 8 } x$ 
B)  $x$ 
C)  1 
D)  8 
A)  $1 + \log _ { 8 } x$ 
B)  $x$ 
C)  1 
D)  8

Question 9

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
-$\log _ { b } \left( \frac { x y ^ { 5 } } { z ^ { 4 } } \right)$

Accepted Answer

A)  $\log _ { \mathrm { b } } \mathrm { x } + 5 \log _ { \mathrm { b } } \mathrm { y } - 4 \log _ { \mathrm { b } } z$ 
B)  $\log _ { b } x + \log _ { b } y ^ { 5 } - \log _ { b } z ^ { 4 }$ 
C)  $\log _ { b } x + 5 \log _ { b } y + 4 \log _ { b } z$ 
D)  $\log _ { \mathrm { b } } \mathrm { x } + \log _ { \mathrm { b } } \mathrm { y } ^ { 5 } + \log _ { \mathrm { b } } \mathrm { z } ^ { 4 }$ 
A)  $\log _ { \mathrm { b } } \mathrm { x } + 5 \log _ { \mathrm { b } } \mathrm { y } - 4 \log _ { \mathrm { b } } z$ 
B)  $\log _ { b } x + \log _ { b } y ^ { 5 } - \log _ { b } z ^ { 4 }$ 
C)  $\log _ { b } x + 5 \log _ { b } y + 4 \log _ { b } z$ 
D)  $\log _ { \mathrm { b } } \mathrm { x } + \log _ { \mathrm { b } } \mathrm { y } ^ { 5 } + \log _ { \mathrm { b } } \mathrm { z } ^ { 4 }$

Question 10

Write the equation in its equivalent logarithmic form.
-$$2 - 2 = \frac { 1 } { 4 }$$

Accepted Answer

A)  $\log _ { 2 } \frac { 1 } { 4 } = 2$ 
B)  $\log _ { 2 } \frac { 1 } { 4 } = - 2$ 
C)  $\log _ { 2 } - 2 = \frac { 1 } { 4 }$ 
D)  $\log _ { 1 / 2 } 2 = - 2$ 
A)  $\log _ { 2 } \frac { 1 } { 4 } = 2$ 
B)  $\log _ { 2 } \frac { 1 } { 4 } = - 2$ 
C)  $\log _ { 2 } - 2 = \frac { 1 } { 4 }$ 
D)  $\log _ { 1 / 2 } 2 = - 2$

Question 11

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
-$\ln \sqrt { \frac { x } { y } }$

Accepted Answer

A)  $\frac { 1 } { 2 } \ln x - \ln y$ 
B)  $\frac { 1 } { 2 } \ln \left( \frac { x } { y } \right)$ 
C)  $\frac { 1 } { 2 } \ln x - \frac { 1 } { 2 } \ln y$ 
D)  $\ln \sqrt { x } - \ln \sqrt { y }$ 
A)  $\frac { 1 } { 2 } \ln x - \ln y$ 
B)  $\frac { 1 } { 2 } \ln \left( \frac { x } { y } \right)$ 
C)  $\frac { 1 } { 2 } \ln x - \frac { 1 } { 2 } \ln y$ 
D)  $\ln \sqrt { x } - \ln \sqrt { y }$

Question 12

Graph the function by making a table of coordinates.
-$f(x)=4^{x}$

Accepted Answer

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

Question 13

Evaluate the expression without using a calculator.
-$\log _ { 10 } \sqrt { 10 }$

Accepted Answer

A)  $\frac { 1 } { 2 }$ 
B)  1 
C)  $\frac { 1 } { 10 }$ 
D)  10 
A)  $\frac { 1 } { 2 }$ 
B)  1 
C)  $\frac { 1 } { 10 }$ 
D)  10

Question 14

Find the domain of the logarithmic function. Write your answer in interval notation.
-$$f ( x ) = \ln ( 4 - x )$$

Accepted Answer

A)  $( - 4 , \infty )$ 
B)  $( - \infty , 4 )$ 
C)  $( - \infty , 0 )$ 
D)  $( - \infty , 4 ) \cup ( 4 , \infty )$ 
A)  $( - 4 , \infty )$ 
B)  $( - \infty , 4 )$ 
C)  $( - \infty , 0 )$ 
D)  $( - \infty , 4 ) \cup ( 4 , \infty )$

Question 15

Evaluate the expression without using a calculator.
-The formula y = 1 + 1.5 ln(x + 1) models the average number of free-throws a basketball player can make consecutively during practice as a function of time, where x is the number of consecutive days the basketball
Player has practiced for two hours. After 13 days of practice, what is the average number of consecutive free
Throws the basketball player makes?

Accepted Answer

A)  5 consecutive free throws 
B)  6 consecutive free throws 
C)  9 consecutive free throws 
D)  8 consecutive free throws 
A)  5 consecutive free throws 
B)  6 consecutive free throws 
C)  9 consecutive free throws 
D)  8 consecutive free throws

Question 16

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
-$\log _ { 2 } ( 7 \cdot 3 )$

Accepted Answer

A)  $\left( \log _ { 2 } 7 \right) \left( \log _ { 2 } 3 \right)$ 
B)  $\log _ { 2 } 7 - \log _ { 2 } 3$ 
C)  $\log _ { 2 } 7 + \log _ { 2 } 3$ 
D)  $\log _ { 2 } 21$ 
A)  $\left( \log _ { 2 } 7 \right) \left( \log _ { 2 } 3 \right)$ 
B)  $\log _ { 2 } 7 - \log _ { 2 } 3$ 
C)  $\log _ { 2 } 7 + \log _ { 2 } 3$ 
D)  $\log _ { 2 } 21$

Question 17

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
-$\log _ { 6 } \left( \frac { 6 } { x } \right)$

Accepted Answer

A)  $1 - \log _ { 6 } x$ 
B)  $\frac { 1 } { x }$ 
C)  $- \log _ { 6 } x$ 
D)  6 
A)  $1 - \log _ { 6 } x$ 
B)  $\frac { 1 } { x }$ 
C)  $- \log _ { 6 } x$ 
D)  6

Question 18

A city has been growing at a rate of 0.5% annually. If there are currently 4,457,000 residents in the city, how many (to the nearest ten-thousand) would be living in this city six years from now? Use the function $$f ( x ) = 4,457,000 ( 2.7 ) ^ { 0.005 t }$$

Accepted Answer

A)  4,620,000 
B)  4,590,000 
C)  360,000 
D)  12,030,000 
A)  4,620,000 
B)  4,590,000 
C)  360,000 
D)  12,030,000

Question 19

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
-$\log _ { 5 } \left( \frac { 25 } { x } \right)$

Accepted Answer

A)  $\frac { 2 } { x }$ 
B)  $2 - \log _ { 5 } x$ 
C)  $- 2 \log _ { 5 } x$ 
D)  $10 - \log _ { 5 } x$ 
A)  $\frac { 2 } { x }$ 
B)  $2 - \log _ { 5 } x$ 
C)  $- 2 \log _ { 5 } x$ 
D)  $10 - \log _ { 5 } x$

Question 20

Graph the function by making a table of coordinates.
-$$f ( x ) = 0.9 ^ { x }$$

Accepted Answer

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

Write the equation in its equivalent exponential form. - $\log _ { 4 } 64 = 3$

The graph of an exponential function is given. Select the function for the graph from the functions listed. -

Use the compound interest formulas A $A = P \left( 1 + \frac { r } { n } \right) ^ { n t }$ and A = Pert to solve. -Find the accumulated value of an investment of $17,000 at 6.5% compounded semiannually for 6 years.

Approximate the number using a calculator. Round the answer to three decimal places. - $\mathrm { e } ^ { - 0.5 }$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\ln \sqrt [ 3 ] { e x }$

The graph of an exponential function is given. Select the function for the graph from the functions listed. -

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 8 } ( 8 x )$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { b } \left( \frac { x y ^ { 5 } } { z ^ { 4 } } \right)$

Write the equation in its equivalent logarithmic form. - $2 - 2 = \frac { 1 } { 4 }$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\ln \sqrt { \frac { x } { y } }$

Graph the function by making a table of coordinates. - $f(x)=4^{x}$ $Graph the function by making a table of coordinates. - f(x)=4^{x}$

Evaluate the expression without using a calculator. - $\log _ { 10 } \sqrt { 10 }$

Find the domain of the logarithmic function. Write your answer in interval notation. - $f ( x ) = \ln ( 4 - x )$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 2 } ( 7 \cdot 3 )$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 6 } \left( \frac { 6 } { x } \right)$

A city has been growing at a rate of 0.5% annually. If there are currently 4,457,000 residents in the city, how many (to the nearest ten-thousand) would be living in this city six years from now? Use the function $f ( x ) = 4,457,000 ( 2.7 ) ^ { 0.005 t }$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 5 } \left( \frac { 25 } { x } \right)$

Graph the function by making a table of coordinates. - $f ( x ) = 0.9 ^ { x }$ $Graph the function by making a table of coordinates. - f ( x ) = 0.9 ^ { x }$

Variables, Real Numbers, and Mathematical Models

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables

Systems of Linear Equations

Exponents and Polynomials

Factoring Polynomials

Rational Expressions

Basics of Functions

Radicals, Radical Functions, and Rational Exponents

Filters

Exam 9: Inequalities and Problem Solving

Write the equation in its equivalent exponential form. - log⁡464=3\log _ { 4 } 64 = 3log4​64=3

The graph of an exponential function is given. Select the function for the graph from the functions listed. -

Use the compound interest formulas A A=P(1+rn)ntA = P \left( 1 + \frac { r } { n } \right) ^ { n t }A=P(1+nr​)nt and A = Pert to solve. -Find the accumulated value of an investment of $17,000 at 6.5% compounded semiannually for 6 years.

Approximate the number using a calculator. Round the answer to three decimal places. - e−0.5\mathrm { e } ^ { - 0.5 }e−0.5

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - ln⁡ex3\ln \sqrt [ 3 ] { e x }ln3ex​

The graph of an exponential function is given. Select the function for the graph from the functions listed. -

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - log⁡8(8x)\log _ { 8 } ( 8 x )log8​(8x)

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - log⁡b(xy5z4)\log _ { b } \left( \frac { x y ^ { 5 } } { z ^ { 4 } } \right)logb​(z4xy5​)

Write the equation in its equivalent logarithmic form. - 2−2=142 - 2 = \frac { 1 } { 4 }2−2=41​

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - ln⁡xy\ln \sqrt { \frac { x } { y } }lnyx​​

Graph the function by making a table of coordinates. - f(x)=4xf(x)=4^{x}f(x)=4x

Evaluate the expression without using a calculator. - log⁡1010\log _ { 10 } \sqrt { 10 }log10​10​

Find the domain of the logarithmic function. Write your answer in interval notation. - f(x)=ln⁡(4−x)f ( x ) = \ln ( 4 - x )f(x)=ln(4−x)

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - log⁡2(7⋅3)\log _ { 2 } ( 7 \cdot 3 )log2​(7⋅3)

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - log⁡6(6x)\log _ { 6 } \left( \frac { 6 } { x } \right)log6​(x6​)

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - log⁡5(25x)\log _ { 5 } \left( \frac { 25 } { x } \right)log5​(x25​)

Graph the function by making a table of coordinates. - f(x)=0.9xf ( x ) = 0.9 ^ { x }f(x)=0.9x

Variables, Real Numbers, and Mathematical Models

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables

Systems of Linear Equations

Exponents and Polynomials

Factoring Polynomials

Rational Expressions

Basics of Functions

Radicals, Radical Functions, and Rational Exponents

Filters

Write the equation in its equivalent exponential form. - $\log _ { 4 } 64 = 3$

Use the compound interest formulas A $A = P \left( 1 + \frac { r } { n } \right) ^ { n t }$ and A = Pert to solve. -Find the accumulated value of an investment of $17,000 at 6.5% compounded semiannually for 6 years.

Approximate the number using a calculator. Round the answer to three decimal places. - $\mathrm { e } ^ { - 0.5 }$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\ln \sqrt [ 3 ] { e x }$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 8 } ( 8 x )$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { b } \left( \frac { x y ^ { 5 } } { z ^ { 4 } } \right)$

Write the equation in its equivalent logarithmic form. - $2 - 2 = \frac { 1 } { 4 }$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\ln \sqrt { \frac { x } { y } }$

Graph the function by making a table of coordinates. - $f(x)=4^{x}$ $Graph the function by making a table of coordinates. - f(x)=4^{x}$

Evaluate the expression without using a calculator. - $\log _ { 10 } \sqrt { 10 }$

Find the domain of the logarithmic function. Write your answer in interval notation. - $f ( x ) = \ln ( 4 - x )$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 2 } ( 7 \cdot 3 )$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 6 } \left( \frac { 6 } { x } \right)$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 5 } \left( \frac { 25 } { x } \right)$

Graph the function by making a table of coordinates. - $f ( x ) = 0.9 ^ { x }$ $Graph the function by making a table of coordinates. - f ( x ) = 0.9 ^ { x }$