Question 1

Evaluate the expression without using a calculator.
-$\log _ { 12 } 1$

Accepted Answer

A)  12 
B)  1 
C)  0 
D)  $\frac { 1 } { 12 }$ 
A)  12 
B)  1 
C)  0 
D)  $\frac { 1 } { 12 }$

Question 2

Evaluate the expression without using a calculator.
-$$5 ^ { \log _ { 5 } 10 }$$

Accepted Answer

A)  10 
B)  5 
C)  $\log _ { 5 } 10$ 
D)  15 
A)  10 
B)  5 
C)  $\log _ { 5 } 10$ 
D)  15

Question 3

Evaluate the expression without using a calculator.
-Use the formula $R = \log \left( \frac { \mathrm { a } } { \mathrm { T } } \right) + \mathrm { B }$ to find the intensity $\mathrm { R }$ on the Richter scale, given that amplitude a is 304 micrometers, time T between waves is $3.8$ seconds, and B is 3.1. Round answer to one decimal place.

Accepted Answer

A)  $1.9$ 
B)  $7.4$ 
C)  $7.5$ 
D)  5 
A)  $1.9$ 
B)  $7.4$ 
C)  $7.5$ 
D)  5

Question 4

Graph the function.
-$$\text { Use the graph of } f ( x ) = 4 ^ { x } \text { to obtain the graph of } g ( x ) = \frac { 1 } { 4 } \cdot 4 ^ { x }$$

Accepted Answer

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

Question 5

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
-$\log _ { 2 } \sqrt [ 4 ] { y }$

Accepted Answer

A)  $\frac { 1 } { 4 } \log _ { 2 } y$ 
B)  $\frac { 1 } { 4 } \log _ { 2 } \sqrt [ 4 ] { y }$ 
C)  $\frac { 1 } { 2 } \log _ { 4 } y$ 
D)  $4 \log _ { 2 } y$ 
A)  $\frac { 1 } { 4 } \log _ { 2 } y$ 
B)  $\frac { 1 } { 4 } \log _ { 2 } \sqrt [ 4 ] { y }$ 
C)  $\frac { 1 } { 2 } \log _ { 4 } y$ 
D)  $4 \log _ { 2 } y$

Question 6

Graph the function by making a table of coordinates.
-$f(x)=\left(\frac{4}{5}\right)^{x}$

Accepted Answer

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

Question 7

Write the equation in its equivalent logarithmic form.
-$4 ^ { 2 } = y$

Accepted Answer

A)  $\log _ { y } 4 = 2$ 
B)  $\log _ { 4 } y = 2$ 
C)  $\log _ { y } 2 = 4$ 
D)  $\log _ { 2 } y = 4$ 
A)  $\log _ { y } 4 = 2$ 
B)  $\log _ { 4 } y = 2$ 
C)  $\log _ { y } 2 = 4$ 
D)  $\log _ { 2 } y = 4$

Question 8

Graph the function by making a table of coordinates.
-$f(x)=\left(\frac{1}{2}\right)^{x}$

Accepted Answer

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

Question 9

The formula S $$S = A \left( \frac { ( 1 + r ) ^ { t + 1 } - 1 } { r } \right)$$ models the value of a retirement account, where A = the number of dollars added to the retirement account each year, r = the annual interest rate, and S = the value of the retirement
Account after t years. If the interest rate is 11%, how much will the account be worth after 15 years if $200 is
Added each year? Round to the nearest whole number.

Accepted Answer

A)  $7838 
B)  $1053 
C)  $15,311 
D)  $3200 
A)  $7838 
B)  $1053 
C)  $15,311 
D)  $3200

Question 10

Evaluate the expression without using a calculator.
-$\log _ { 8 } 8$

Accepted Answer

A)  1 
B)  $\frac { 1 } { 8 }$ 
C)  0 
D)  8 
A)  1 
B)  $\frac { 1 } { 8 }$ 
C)  0 
D)  8

Question 11

Solve.
-The rabbit population in a forest area grows at the rate of 8% monthly. If there are 260 rabbits in September, find how many rabbits (rounded to the nearest whole number) should be expected by next September. Use the
Function f(x) $$f ( x ) = 260 ( 2.7 ) ^ { 0.08 t }$$

Accepted Answer

A)  688 rabbits 
B)  662 rabbits 
C)  674 rabbits 
D)  675 rabbits 
A)  688 rabbits 
B)  662 rabbits 
C)  674 rabbits 
D)  675 rabbits

Question 12

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

Accepted Answer

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

Question 13

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 $20,000 at 5.75% compounded annually for 7 years.

Accepted Answer

A)  $27,971.27 
B)  $29,579.62 
C)  $26,900.00 
D)  $28,050.00 
A)  $27,971.27 
B)  $29,579.62 
C)  $26,900.00 
D)  $28,050.00

Question 14

Evaluate the expression without using a calculator.
-$$\log _ { 10 } 10,000$$

Accepted Answer

A)  $- 4$ 
B)  40 
C)  4 
D)  $\frac { 1 } { 10000 }$ 
A)  $- 4$ 
B)  40 
C)  4 
D)  $\frac { 1 } { 10000 }$

Question 15

Evaluate the expression without using a calculator.
-$\log _ { 7 } 7 ^ { 10 }$

Accepted Answer

A)  17 
B)  10 
C)  $\log _ { 7 } 10$ 
D)  7 
A)  17 
B)  10 
C)  $\log _ { 7 } 10$ 
D)  7

Question 16

Find the domain of the logarithmic function. Write your answer in interval notation.
-$$f ( x ) = \log ( x - 6 )$$

Accepted Answer

A)  $( - \infty , 0 ) \cup ( 0 , \infty )$ 
B)  $( - 6 , \infty )$ 
C)  $( - \infty , 6 ) \cup ( 6 , \infty )$ 
D)  $( 6 , \infty )$ 
A)  $( - \infty , 0 ) \cup ( 0 , \infty )$ 
B)  $( - 6 , \infty )$ 
C)  $( - \infty , 6 ) \cup ( 6 , \infty )$ 
D)  $( 6 , \infty )$

Question 17

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

Accepted Answer

A)  $z \ln y$ 
B)  $- z \ln y$ 
C)  $y \ln z$ 
D)  $- y \ln z$ 
A)  $z \ln y$ 
B)  $- z \ln y$ 
C)  $y \ln z$ 
D)  $- y \ln z$

Question 18

Graph the function.
-$$\text { Use the graph of } f ( x ) = 2 ^ { x } \text { to obtain the graph of } g ( x ) = 2 ^ { x } + 1 \text {. }$$

Accepted Answer

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

Question 19

Approximate the number using a calculator. Round the answer to three decimal places.
-$$4 ^ { 1.1 }$$

Accepted Answer

A)  1.464 
B)  4.895 
C)  4.400 
D)  4.595 
A)  1.464 
B)  4.895 
C)  4.400 
D)  4.595

Question 20

Graph the function.
-Use the graph of $f ( x ) = 3 ^ { x }$ to obtain the graph of $g ( x ) = 3 ^ { x } + 3 + 1$

Accepted Answer

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

Evaluate the expression without using a calculator. - $\log _ { 12 } 1$

Evaluate the expression without using a calculator. - $5 ^ { \log _ { 5 } 10 }$

Graph the function. - $\text { Use the graph of } f ( x ) = 4 ^ { x } \text { to obtain the graph of } g ( x ) = \frac { 1 } { 4 } \cdot 4 ^ { x }$ $Graph the function. - \text { Use the graph of } f ( x ) = 4 ^ { x } \text { to obtain the graph of } g ( x ) = \frac { 1 } { 4 } \cdot 4 ^ { x }$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 2 } \sqrt [ 4 ] { y }$

Graph the function by making a table of coordinates. - $f(x)=\left(\frac{4}{5}\right)^{x}$ $Graph the function by making a table of coordinates. - f(x)=\left(\frac{4}{5}\right)^{x}$

Write the equation in its equivalent logarithmic form. - $4 ^ { 2 } = y$

Graph the function by making a table of coordinates. - $f(x)=\left(\frac{1}{2}\right)^{x}$ $Graph the function by making a table of coordinates. - f(x)=\left(\frac{1}{2}\right)^{x}$

Evaluate the expression without using a calculator. - $\log _ { 8 } 8$

Solve. -The rabbit population in a forest area grows at the rate of 8% monthly. If there are 260 rabbits in September, find how many rabbits (rounded to the nearest whole number) should be expected by next September. Use the Function f(x) $f ( x ) = 260 ( 2.7 ) ^ { 0.08 t }$

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 $20,000 at 5.75% compounded annually for 7 years.

Evaluate the expression without using a calculator. - $\log _ { 10 } 10,000$

Evaluate the expression without using a calculator. - $\log _ { 7 } 7 ^ { 10 }$

Find the domain of the logarithmic function. Write your answer in interval notation. - $f ( x ) = \log ( x - 6 )$

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

Graph the function. - $\text { Use the graph of } f ( x ) = 2 ^ { x } \text { to obtain the graph of } g ( x ) = 2 ^ { x } + 1 \text {. }$ $Graph the function. - \text { Use the graph of } f ( x ) = 2 ^ { x } \text { to obtain the graph of } g ( x ) = 2 ^ { x } + 1 \text {. }$

Approximate the number using a calculator. Round the answer to three decimal places. - $4 ^ { 1.1 }$

Graph the function. -Use the graph of $f ( x ) = 3 ^ { x }$ to obtain the graph of $g ( x ) = 3 ^ { x } + 3 + 1$ $Graph the function. -Use the graph of f ( x ) = 3 ^ { x } to obtain the graph of g ( x ) = 3 ^ { x } + 3 + 1$

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

Evaluate the expression without using a calculator. - log⁡121\log _ { 12 } 1log12​1

Evaluate the expression without using a calculator. - 5log⁡5105 ^ { \log _ { 5 } 10 }5log5​10

Graph the function. - Use the graph of f(x)=4x to obtain the graph of g(x)=14⋅4x\text { Use the graph of } f ( x ) = 4 ^ { x } \text { to obtain the graph of } g ( x ) = \frac { 1 } { 4 } \cdot 4 ^ { x } Use the graph of f(x)=4x to obtain the graph of g(x)=41​⋅4x

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - log⁡2y4\log _ { 2 } \sqrt [ 4 ] { y }log2​4y​

Graph the function by making a table of coordinates. - f(x)=(45)xf(x)=\left(\frac{4}{5}\right)^{x}f(x)=(54​)x

Write the equation in its equivalent logarithmic form. - 42=y4 ^ { 2 } = y42=y

Graph the function by making a table of coordinates. - f(x)=(12)xf(x)=\left(\frac{1}{2}\right)^{x}f(x)=(21​)x

Evaluate the expression without using a calculator. - log⁡88\log _ { 8 } 8log8​8

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 $20,000 at 5.75% compounded annually for 7 years.

Evaluate the expression without using a calculator. - log⁡1010,000\log _ { 10 } 10,000log10​10,000

Evaluate the expression without using a calculator. - log⁡7710\log _ { 7 } 7 ^ { 10 }log7​710

Find the domain of the logarithmic function. Write your answer in interval notation. - f(x)=log⁡(x−6)f ( x ) = \log ( x - 6 )f(x)=log(x−6)

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - ln⁡y−z\ln y ^ { - z }lny−z

Graph the function. - Use the graph of f(x)=2x to obtain the graph of g(x)=2x+1. \text { Use the graph of } f ( x ) = 2 ^ { x } \text { to obtain the graph of } g ( x ) = 2 ^ { x } + 1 \text {. } Use the graph of f(x)=2x to obtain the graph of g(x)=2x+1.

Approximate the number using a calculator. Round the answer to three decimal places. - 41.14 ^ { 1.1 }41.1

Graph the function. -Use the graph of f(x)=3xf ( x ) = 3 ^ { x }f(x)=3x to obtain the graph of g(x)=3x+3+1g ( x ) = 3 ^ { x } + 3 + 1g(x)=3x+3+1

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

Evaluate the expression without using a calculator. - $\log _ { 12 } 1$

Evaluate the expression without using a calculator. - $5 ^ { \log _ { 5 } 10 }$

Graph the function. - $\text { Use the graph of } f ( x ) = 4 ^ { x } \text { to obtain the graph of } g ( x ) = \frac { 1 } { 4 } \cdot 4 ^ { x }$ $Graph the function. - \text { Use the graph of } f ( x ) = 4 ^ { x } \text { to obtain the graph of } g ( x ) = \frac { 1 } { 4 } \cdot 4 ^ { x }$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 2 } \sqrt [ 4 ] { y }$

Graph the function by making a table of coordinates. - $f(x)=\left(\frac{4}{5}\right)^{x}$ $Graph the function by making a table of coordinates. - f(x)=\left(\frac{4}{5}\right)^{x}$

Write the equation in its equivalent logarithmic form. - $4 ^ { 2 } = y$

Graph the function by making a table of coordinates. - $f(x)=\left(\frac{1}{2}\right)^{x}$ $Graph the function by making a table of coordinates. - f(x)=\left(\frac{1}{2}\right)^{x}$

Evaluate the expression without using a calculator. - $\log _ { 8 } 8$

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 $20,000 at 5.75% compounded annually for 7 years.

Evaluate the expression without using a calculator. - $\log _ { 10 } 10,000$

Evaluate the expression without using a calculator. - $\log _ { 7 } 7 ^ { 10 }$

Find the domain of the logarithmic function. Write your answer in interval notation. - $f ( x ) = \log ( x - 6 )$

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

Graph the function. - $\text { Use the graph of } f ( x ) = 2 ^ { x } \text { to obtain the graph of } g ( x ) = 2 ^ { x } + 1 \text {. }$ $Graph the function. - \text { Use the graph of } f ( x ) = 2 ^ { x } \text { to obtain the graph of } g ( x ) = 2 ^ { x } + 1 \text {. }$

Approximate the number using a calculator. Round the answer to three decimal places. - $4 ^ { 1.1 }$

Graph the function. -Use the graph of $f ( x ) = 3 ^ { x }$ to obtain the graph of $g ( x ) = 3 ^ { x } + 3 + 1$ $Graph the function. -Use the graph of f ( x ) = 3 ^ { x } to obtain the graph of g ( x ) = 3 ^ { x } + 3 + 1$