Question 1

Write the equation in its equivalent logarithmic form.
-$$5 ^ { 2 } = 25$$

Accepted Answer

A)  $\log _ { 25 } 5 = 2$ 
B)  $\log _ { 5 } 25 = 2$ 
C)  $\log _ { 2 } 25 = 5$ 
D)  $\log _ { 5 } 2 = 25$ 
A)  $\log _ { 25 } 5 = 2$ 
B)  $\log _ { 5 } 25 = 2$ 
C)  $\log _ { 2 } 25 = 5$ 
D)  $\log _ { 5 } 2 = 25$

Question 2

Graph the function.
-Use the graph of $f ( x ) = 5 ^ { x }$ to obtain the graph of $g ( x ) = 5 ^ { x } + 2$

Accepted Answer

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

Question 3

Graph the function.
-Use the graph of $f ( x ) = 4 ^ { x }$ to obtain the graph of $g ( x ) = 4 ^ { x - 3 }$

Accepted Answer

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

Question 4

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

Accepted Answer

A)  $f ( x ) = 3 ^ { x }$ 
B)  $f ( x ) = 3 ^ { - x }$ 
C)  $f ( x ) = - 3 ^ { x }$ 
D)  $f ( x ) = - 3 ^ { - x }$ 
A)  $f ( x ) = 3 ^ { x }$ 
B)  $f ( x ) = 3 ^ { - x }$ 
C)  $f ( x ) = - 3 ^ { x }$ 
D)  $f ( x ) = - 3 ^ { - x }$

Question 5

Evaluate the expression without using a calculator.
-$\log \left( \frac { 1 } { 10,000 } \right)$

Accepted Answer

A)  $- \frac { 1 } { 4 }$ 
B)  $\frac { 1 } { 10,000 }$ 
C)  $- 4$ 
D)  4 
A)  $- \frac { 1 } { 4 }$ 
B)  $\frac { 1 } { 10,000 }$ 
C)  $- 4$ 
D)  4

Question 6

Evaluate the expression without using a calculator.
-$\log _ { 5 } 25$

Accepted Answer

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

Question 7

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
-$\log _ { 3 } \left( \frac { 81 } { \sqrt { x - 1 } } \right)$

Accepted Answer

A)  $4 \log _ { 3 } 3 - \frac { 1 } { 2 } \log _ { 3 } ( x - 1 )$ 
B)  $\log _ { 3 } 81 - \log _ { 3 } \sqrt { x - 1 }$ 
C)  $4 - \log _ { 3 } \sqrt { x - 1 }$ 
D)  $4 - \frac { 1 } { 2 } \log _ { 3 } ( x - 1 )$ 
A)  $4 \log _ { 3 } 3 - \frac { 1 } { 2 } \log _ { 3 } ( x - 1 )$ 
B)  $\log _ { 3 } 81 - \log _ { 3 } \sqrt { x - 1 }$ 
C)  $4 - \log _ { 3 } \sqrt { x - 1 }$ 
D)  $4 - \frac { 1 } { 2 } \log _ { 3 } ( x - 1 )$

Question 8

Evaluate the expression without using a calculator.
-$\log _ { 25 } 5$

Accepted Answer

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

Question 9

Write the equation in its equivalent exponential form.
-$$3 = \log _ { 2 } x$$

Accepted Answer

A)  $2 ^ { 3 } = x$ 
B)  $3 ^ { 2 } = x$ 
C)  $x ^ { 3 } = 2$ 
D)  $2 ^ { x } = 3$ 
A)  $2 ^ { 3 } = x$ 
B)  $3 ^ { 2 } = x$ 
C)  $x ^ { 3 } = 2$ 
D)  $2 ^ { x } = 3$

Question 10

Graph the function.
-Use the graph of $f ( x ) = 5 ^ { x }$ to obtain the graph of $g ( x ) = - 5 ^ { x }$.

Accepted Answer

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

Question 11

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 $1800 at 8% compounded quarterly for 2 years.

Accepted Answer

A)  $1872.72 
B)  $2099.52 
C)  $2088.00 
D)  $2108.99 
A)  $1872.72 
B)  $2099.52 
C)  $2088.00 
D)  $2108.99

Question 12

Write the equation in its equivalent logarithmic form.
-$$4 ^ { x } = 64$$

Accepted Answer

A)  $\log _ { 64 } x = 4$ 
B)  $\log _ { x } 64 = 4$ 
C)  $\log _ { 4 } 64 = x$ 
D)  $\log _ { 64 } 4 = x$ 
A)  $\log _ { 64 } x = 4$ 
B)  $\log _ { x } 64 = 4$ 
C)  $\log _ { 4 } 64 = x$ 
D)  $\log _ { 64 } 4 = x$

Question 13

Evaluate the expression without using a calculator.
-$$\log _ { 3 } \frac { 1 } { 27 }$$

Accepted Answer

A)  9 
B)  3 
C)  $\frac { 1 } { 3 }$ 
D)  $- 3$ 
A)  9 
B)  3 
C)  $\frac { 1 } { 3 }$ 
D)  $- 3$

Question 14

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 $5000 at 7% compounded continuously for 6 years.

Accepted Answer

A)  $7709.81 
B)  $7609.81 
C)  $7100.00 
D)  $7503.65 
A)  $7709.81 
B)  $7609.81 
C)  $7100.00 
D)  $7503.65

Question 15

Approximate the number using a calculator. Round the answer to three decimal places.
-$$6^{\sqrt{3}}$$

Accepted Answer

A)  22.274 
B)  108.000 
C)  27.000 
D)  10.392 
A)  22.274 
B)  108.000 
C)  27.000 
D)  10.392

Question 16

Evaluate the expression without using a calculator.
-$\log 10 ^ { 3 }$

Accepted Answer

A)  $10 ^ { 3 }$ 
B)  $\log 3$ 
C)  10 
D)  3 
A)  $10 ^ { 3 }$ 
B)  $\log 3$ 
C)  10 
D)  3

Question 17

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 $1080 at 6.5% compounded annually for 7 years.

Accepted Answer

A)  $1575.87 
B)  $1501.20 
C)  $1678.31 
D)  $1571.40 
A)  $1575.87 
B)  $1501.20 
C)  $1678.31 
D)  $1571.40

Question 18

Evaluate the expression without using a calculator.
-The pH of a solution ranges from 0 to 14. An acid has a pH less than 7. Pure water is neutral and has a pH of 7. The pH of a solution is given by pH = -log x where x represents the concentration of the hydrogen ions in the
Solution in moles per liter. Find the pH if the hydrogen ion concentration is 1 × 10-6.

Accepted Answer

A)  8 
B)  -8 
C)  6 
D)  -6 
A)  8 
B)  -8 
C)  6 
D)  -6

Question 19

Find the domain of the logarithmic function. Write your answer in interval notation.
-$$f ( x ) = \log _ { 4 } ( x - 8 ) ^ { 2 }$$

Accepted Answer

A)  $( 8 , \infty )$ 
B)  $( - 8 , \infty )$ 
C)  $( - \infty , 0 ) \cup ( 0 , \infty )$ 
D)  $( - \infty , 8 ) \cup ( 8 , \infty )$ 
A)  $( 8 , \infty )$ 
B)  $( - 8 , \infty )$ 
C)  $( - \infty , 0 ) \cup ( 0 , \infty )$ 
D)  $( - \infty , 8 ) \cup ( 8 , \infty )$

Question 20

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
-$\log \left( \frac { x } { 100 } \right)$

Accepted Answer

A)  $\log x + 2$ 
B)  $100 x$ 
C)  $\log x - 2$ 
D)  $- 20 x$ 
A)  $\log x + 2$ 
B)  $100 x$ 
C)  $\log x - 2$ 
D)  $- 20 x$

Write the equation in its equivalent logarithmic form. - $5 ^ { 2 } = 25$

Graph the function. -Use the graph of $f ( x ) = 5 ^ { x }$ to obtain the graph of $g ( x ) = 5 ^ { x } + 2$ $Graph the function. -Use the graph of f ( x ) = 5 ^ { x } to obtain the graph of g ( x ) = 5 ^ { x } + 2$

Graph the function. -Use the graph of $f ( x ) = 4 ^ { x }$ to obtain the graph of $g ( x ) = 4 ^ { x - 3 }$ $Graph the function. -Use the graph of f ( x ) = 4 ^ { x } to obtain the graph of g ( x ) = 4 ^ { x - 3 }$

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

Evaluate the expression without using a calculator. - $\log \left( \frac { 1 } { 10,000 } \right)$

Evaluate the expression without using a calculator. - $\log _ { 5 } 25$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 3 } \left( \frac { 81 } { \sqrt { x - 1 } } \right)$

Evaluate the expression without using a calculator. - $\log _ { 25 } 5$

Write the equation in its equivalent exponential form. - $3 = \log _ { 2 } x$

Graph the function. -Use the graph of $f ( x ) = 5 ^ { x }$ to obtain the graph of $g ( x ) = - 5 ^ { x }$ . $Graph the function. -Use the graph of f ( x ) = 5 ^ { x } to obtain the graph of g ( x ) = - 5 ^ { x } .$

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 $1800 at 8% compounded quarterly for 2 years.

Write the equation in its equivalent logarithmic form. - $4 ^ { x } = 64$

Evaluate the expression without using a calculator. - $\log _ { 3 } \frac { 1 } { 27 }$

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 $5000 at 7% compounded continuously for 6 years.

Approximate the number using a calculator. Round the answer to three decimal places. - $6^{\sqrt{3}}$

Evaluate the expression without using a calculator. - $\log 10 ^ { 3 }$

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 $1080 at 6.5% compounded annually for 7 years.

Find the domain of the logarithmic function. Write your answer in interval notation. - $f ( x ) = \log _ { 4 } ( x - 8 ) ^ { 2 }$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log \left( \frac { x } { 100 } \right)$

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 logarithmic form. - 52=255 ^ { 2 } = 2552=25

Graph the function. -Use the graph of f(x)=5xf ( x ) = 5 ^ { x }f(x)=5x to obtain the graph of g(x)=5x+2g ( x ) = 5 ^ { x } + 2g(x)=5x+2

Graph the function. -Use the graph of f(x)=4xf ( x ) = 4 ^ { x }f(x)=4x to obtain the graph of g(x)=4x−3g ( x ) = 4 ^ { x - 3 }g(x)=4x−3

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

Evaluate the expression without using a calculator. - log⁡(110,000)\log \left( \frac { 1 } { 10,000 } \right)log(10,0001​)

Evaluate the expression without using a calculator. - log⁡525\log _ { 5 } 25log5​25

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - log⁡3(81x−1)\log _ { 3 } \left( \frac { 81 } { \sqrt { x - 1 } } \right)log3​(x−1​81​)

Evaluate the expression without using a calculator. - log⁡255\log _ { 25 } 5log25​5

Write the equation in its equivalent exponential form. - 3=log⁡2x3 = \log _ { 2 } x3=log2​x

Graph the function. -Use the graph of f(x)=5xf ( x ) = 5 ^ { x }f(x)=5x to obtain the graph of g(x)=−5xg ( x ) = - 5 ^ { x }g(x)=−5x .

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 $1800 at 8% compounded quarterly for 2 years.

Write the equation in its equivalent logarithmic form. - 4x=644 ^ { x } = 644x=64

Evaluate the expression without using a calculator. - log⁡3127\log _ { 3 } \frac { 1 } { 27 }log3​271​

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 $5000 at 7% compounded continuously for 6 years.

Approximate the number using a calculator. Round the answer to three decimal places. - 636^{\sqrt{3}}63​

Evaluate the expression without using a calculator. - log⁡103\log 10 ^ { 3 }log103

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 $1080 at 6.5% compounded annually for 7 years.

Find the domain of the logarithmic function. Write your answer in interval notation. - f(x)=log⁡4(x−8)2f ( x ) = \log _ { 4 } ( x - 8 ) ^ { 2 }f(x)=log4​(x−8)2

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - log⁡(x100)\log \left( \frac { x } { 100 } \right)log(100x​)