Question 1

Solve.
-$\log _ { a } 1000 = 3$

Accepted Answer

A)  $a = 1000$ 
B)  $a = 10$ 
C)  $a = 3$ 
D)  $a = 10 ^ { 3 }$ 
A)  $a = 1000$ 
B)  $a = 10$ 
C)  $a = 3$ 
D)  $a = 10 ^ { 3 }$

Question 2

Graph the function.
-$$f ( x ) = e ^ { x - 1 }$$

Accepted Answer

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

Question 3

Write the expression as the sum or difference of single logarithms.
-$\log _ { 10 } \left( \frac { \sqrt [ 3 ] { 17 } } { x ^ { 2 } y } \right)$

Accepted Answer

A)  $\frac { 1 } { 3 } \log _ { 10 } 17 - 2 \log _ { 10 } x - 2 \log _ { 10 } y$ 
B)  $\frac { 1 } { 3 } \log _ { 10 } 17 - 2 \log _ { 10 } x - \log _ { 10 } y$ 
C)  $3 \log _ { 10 } 17 - 2 \log _ { 10 } x - \log _ { 10 } 3$ 
D)  $\log _ { 10 } 17 - \log _ { 10 } x - \log _ { 10 } y$ 
A)  $\frac { 1 } { 3 } \log _ { 10 } 17 - 2 \log _ { 10 } x - 2 \log _ { 10 } y$ 
B)  $\frac { 1 } { 3 } \log _ { 10 } 17 - 2 \log _ { 10 } x - \log _ { 10 } y$ 
C)  $3 \log _ { 10 } 17 - 2 \log _ { 10 } x - \log _ { 10 } 3$ 
D)  $\log _ { 10 } 17 - \log _ { 10 } x - \log _ { 10 } y$

Question 4

Evaluate.
-$\log _ { 11 } 1$

Accepted Answer

A)  $x = 1$ 
B)  $x = 11$ 
C)  $x = \frac { 1 } { 11 }$ 
D)  $x = 0$ 
A)  $x = 1$ 
B)  $x = 11$ 
C)  $x = \frac { 1 } { 11 }$ 
D)  $x = 0$

Question 5

Graph the function.
-$f(x)=2^{x}$

Accepted Answer

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

Question 6

Write in logarithmic form.
-$$\frac { 1 } { 16 } = 4 ^ { - 2 }$$

Accepted Answer

A)  $\log _ { 4 } \frac { 1 } { 16 } = - 2$ 
B)  $\log _ { - 2 } \frac { 1 } { 16 } = 4$ 
C)  $\log _ { 1 / 16 } 4 = - 2$ 
D)  $\log _ { 4 } - 2 = \frac { 1 } { 16 }$ 
A)  $\log _ { 4 } \frac { 1 } { 16 } = - 2$ 
B)  $\log _ { - 2 } \frac { 1 } { 16 } = 4$ 
C)  $\log _ { 1 / 16 } 4 = - 2$ 
D)  $\log _ { 4 } - 2 = \frac { 1 } { 16 }$

Question 7

A solution is an acid if its pH is less than 7 and a base if its pH is greater than 7. The pH is defined by pH = -log10[H+],
where [H+] is the concentration of hydrogen ions in the solution. Use this information to answer the question
-The concentration of hydrogen ions in a solution is approximately $10 ^ { - 6.1 }$. What is the pH of the solution? Is the solution an acid or a base?

Accepted Answer

A)  The $\mathrm { pH }$ is 6.1. The solution is an acid. 
B)  The pH is 6.1. The solution is a base. 
C)  The $\mathrm { pH }$ is -6.1. The solution is a base. 
D)  The $\mathrm { pH }$ is -6.1. The solution is an acid. 
A)  The $\mathrm { pH }$ is 6.1. The solution is an acid. 
B)  The pH is 6.1. The solution is a base. 
C)  The $\mathrm { pH }$ is -6.1. The solution is a base. 
D)  The $\mathrm { pH }$ is -6.1. The solution is an acid.

Question 8

Solve for x.
-The rabbit population in a forest area grows at the rate of 7% monthly. If there are 180 rabbits in September, find how many rabbits (rounded to the nearest whole number)should be expected by next September. Use The radioactive decay of radium 226 can be described by the equation $\mathrm { A } = \mathrm { Ce } - 0.0004279 \mathrm { t }$, where $\mathrm { C }$ is the original amount of radium and $\mathrm { A }$ is the amount of radium remaining after $\mathrm { t }$ years. If 22 milligrams of radium are sealed in a container now, how much radium will be in the container after 100 years. Round to the nearest thousand th.

Accepted Answer

A)  $1.191 \mathrm { mg }$ 
B)  $21.991 \mathrm { mg }$ 
C)  $21.078 \mathrm { mg }$ 
D)  $22.962 \mathrm { mg }$ 
A)  $1.191 \mathrm { mg }$ 
B)  $21.991 \mathrm { mg }$ 
C)  $21.078 \mathrm { mg }$ 
D)  $22.962 \mathrm { mg }$

Question 9

Solve.
-$\log _ { 25 } 5 = w$

Accepted Answer

A)  $w = 2$ 
B)  $w = \frac { 1 } { 2 }$ 
C)  $w = 25$ 
D)  $w = 5$ 
A)  $w = 2$ 
B)  $w = \frac { 1 } { 2 }$ 
C)  $w = 25$ 
D)  $w = 5$

Question 10

Solve for x.
-How much money will Lyle have in 6 years is he invests $\$ 9000$ at $17 \%$ annual rate of interest compounded quarterly? How much will he have if it is compounded monthly? Use the interest formula $\mathrm { A } = \mathrm { P } \left( 1 + \frac { \mathrm { r } } { \mathrm { n } } \right) ^ { \mathrm { n } t }$. Round the answers to the nearest cent.

Accepted Answer

A)  $\$ 9964.30$ when compounded quarterly
$\$ 9965.73$ when compounded monthly 
B)  $\$ 24,438.13$ when compounded quarterly 
 $\$ 67,279.74$ when compounded monthly 
C)  $\$ 9964.30$ when compounded quarterly
 $\$ 24,780.75$ when compounded monthly 
D)  $\$ 24,438.13$ when compounded quarterly
$\$ 24,780.75$ when compounded monthly 
A)  $\$ 9964.30$ when compounded quarterly
$\$ 9965.73$ when compounded monthly 
B)  $\$ 24,438.13$ when compounded quarterly 
 $\$ 67,279.74$ when compounded monthly 
C)  $\$ 9964.30$ when compounded quarterly
 $\$ 24,780.75$ when compounded monthly 
D)  $\$ 24,438.13$ when compounded quarterly
$\$ 24,780.75$ when compounded monthly

Question 11

Write in exponential form.
-$$0 = \log _ { 13 } 1$$

Accepted Answer

A)  $13 ^ { 0 } = 1$ 
B)  $1 ^ { 13 } = 0$ 
C)  $0 ^ { 13 } = 1$ 
D)  does not exist 
A)  $13 ^ { 0 } = 1$ 
B)  $1 ^ { 13 } = 0$ 
C)  $0 ^ { 13 } = 1$ 
D)  does not exist

Question 12

Write in logarithmic form.
-$$343 = 7 ^ { 3 }$$

Accepted Answer

A)  $\log _ { 7 } 343 = 3$ 
B)  $\log _ { 3 } 343 = 7$ 
C)  $\log _ { 7 } 3 = 343$ 
D)  $\log _ { 343 } 7 = 3$ 
A)  $\log _ { 7 } 343 = 3$ 
B)  $\log _ { 3 } 343 = 7$ 
C)  $\log _ { 7 } 3 = 343$ 
D)  $\log _ { 343 } 7 = 3$

Question 13

Express as a sum of logarithms.
-$\log _ { 4 } ( 5 \cdot 11 )$

Accepted Answer

A)  $\log 5 + \log 11 + \log 4$ 
B)  $\log ( 5 + 11 + 4 )$ 
C)  $\log _ { 4 } 5 + \log _ { 4 } 11$ 
D)  $\log _ { 2 } 5 + \log _ { 2 } 11$ 
A)  $\log 5 + \log 11 + \log 4$ 
B)  $\log ( 5 + 11 + 4 )$ 
C)  $\log _ { 4 } 5 + \log _ { 4 } 11$ 
D)  $\log _ { 2 } 5 + \log _ { 2 } 11$

Question 14

Solve.
-$$\log _ { 4 } \frac { 1 } { 64 } = x$$

Accepted Answer

A)  $x = - 3$ 
B)  $x = \frac { 1 } { 256 }$ 
C)  $ x = \frac { 1 } { 16 }$ 
D)  $x = 3$ 
A)  $x = - 3$ 
B)  $x = \frac { 1 } { 256 }$ 
C)  $ x = \frac { 1 } { 16 }$ 
D)  $x = 3$

Question 15

Graph the function.
-$$f ( x ) = 4 ^ { - x }$$

Accepted Answer

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

Question 16

Solve for x.
-$$4 ^ { - x } = \frac { 1 } { 16 }$$

Accepted Answer

A)  $x = 2$ 
B)  $x = \frac { 1 } { 2 }$ 
C)  $x = - 2$ 
D)  $x = \frac { 1 } { 4 }$ 
A)  $x = 2$ 
B)  $x = \frac { 1 } { 2 }$ 
C)  $x = - 2$ 
D)  $x = \frac { 1 } { 4 }$

Question 17

Evaluate.
-$2 ^ { \log _ { 2 } 13 }$

Accepted Answer

A)  $x = 15$ 
B)  $x = \log _ { 2 } 13$ 
C)  $x = 13$ 
D)  $x = 2$ 
A)  $x = 15$ 
B)  $x = \log _ { 2 } 13$ 
C)  $x = 13$ 
D)  $x = 2$

Question 18

Write in exponential form.
-$$\frac { 1 } { 2 } = \log _ { 16 } 4$$

Accepted Answer

A)  $16 ^ { 4 } = \frac { 1 } { 2 }$ 
B)  $4 ^ { 1 / 2 } = 16$ 
C)  $16 ^ { 1 / 2 } = 4$ 
D)  $\left( \frac { 1 } { 2 } \right) ^ { 16 } = 4$ 
A)  $16 ^ { 4 } = \frac { 1 } { 2 }$ 
B)  $4 ^ { 1 / 2 } = 16$ 
C)  $16 ^ { 1 / 2 } = 4$ 
D)  $\left( \frac { 1 } { 2 } \right) ^ { 16 } = 4$

Question 19

Solve.
-$$\log _ { 3 } x = - 2$$

Accepted Answer

A)  $x = 1$ 
B)  $x = - 6$ 
C)  $x = \frac { 1 } { 8 }$ 
D)  $x = \frac { 1 } { 9 }$ 
A)  $x = 1$ 
B)  $x = - 6$ 
C)  $x = \frac { 1 } { 8 }$ 
D)  $x = \frac { 1 } { 9 }$

Question 20

Express as a sum of logarithms.
-$\log _ { 10 } x y$

Accepted Answer

A)  $\log _ { 5 } x - \log _ { 5 } y$ 
B)  $\log _ { 10 } x + \log _ { 10 } y$ 
C)  $\log _ { 5 } x + \log _ { 5 } y$ 
D)  $\log _ { 10 } x - \log _ { 10 } y$ 
A)  $\log _ { 5 } x - \log _ { 5 } y$ 
B)  $\log _ { 10 } x + \log _ { 10 } y$ 
C)  $\log _ { 5 } x + \log _ { 5 } y$ 
D)  $\log _ { 10 } x - \log _ { 10 } y$

Solve. - $\log _ { a } 1000 = 3$

Graph the function. - $f ( x ) = e ^ { x - 1 }$ $Graph the function. - f ( x ) = e ^ { x - 1 }$

Write the expression as the sum or difference of single logarithms. - $\log _ { 10 } \left( \frac { \sqrt [ 3 ] { 17 } } { x ^ { 2 } y } \right)$

Evaluate. - $\log _ { 11 } 1$

Graph the function. - $f(x)=2^{x}$ $Graph the function. - f(x)=2^{x}$

Write in logarithmic form. - $\frac { 1 } { 16 } = 4 ^ { - 2 }$

Solve. - $\log _ { 25 } 5 = w$

Write in exponential form. - $0 = \log _ { 13 } 1$

Write in logarithmic form. - $343 = 7 ^ { 3 }$

Express as a sum of logarithms. - $\log _ { 4 } ( 5 \cdot 11 )$

Solve. - $\log _ { 4 } \frac { 1 } { 64 } = x$

Graph the function. - $f ( x ) = 4 ^ { - x }$ $Graph the function. - f ( x ) = 4 ^ { - x }$

Solve for x. - $4 ^ { - x } = \frac { 1 } { 16 }$

Evaluate. - $2 ^ { \log _ { 2 } 13 }$

Write in exponential form. - $\frac { 1 } { 2 } = \log _ { 16 } 4$

Solve. - $\log _ { 3 } x = - 2$

Express as a sum of logarithms. - $\log _ { 10 } x y$

Real Numbers and Variables

Equations, Inequalities, and Applications

Graphing and Functions

Systems of Linear Equations and Inequalities

Exponents and Polynomials

Factoring

Rational Expressions and Equations

Rational Exponents and Radicals

Quadratic Equations and Inequalities

The Conic Sections

Additional Properties of Functions

Filters

Exam 12: Logarithmic and Exponential Functions

Solve. - log⁡a1000=3\log _ { a } 1000 = 3loga​1000=3

Graph the function. - f(x)=ex−1f ( x ) = e ^ { x - 1 }f(x)=ex−1

Write the expression as the sum or difference of single logarithms. - log⁡10(173x2y)\log _ { 10 } \left( \frac { \sqrt [ 3 ] { 17 } } { x ^ { 2 } y } \right)log10​(x2y317​​)

Evaluate. - log⁡111\log _ { 11 } 1log11​1

Graph the function. - f(x)=2xf(x)=2^{x}f(x)=2x

Write in logarithmic form. - 116=4−2\frac { 1 } { 16 } = 4 ^ { - 2 }161​=4−2

Solve. - log⁡255=w\log _ { 25 } 5 = wlog25​5=w

Write in exponential form. - 0=log⁡1310 = \log _ { 13 } 10=log13​1

Write in logarithmic form. - 343=73343 = 7 ^ { 3 }343=73

Express as a sum of logarithms. - log⁡4(5⋅11)\log _ { 4 } ( 5 \cdot 11 )log4​(5⋅11)

Solve. - log⁡4164=x\log _ { 4 } \frac { 1 } { 64 } = xlog4​641​=x

Graph the function. - f(x)=4−xf ( x ) = 4 ^ { - x }f(x)=4−x

Solve for x. - 4−x=1164 ^ { - x } = \frac { 1 } { 16 }4−x=161​

Evaluate. - 2log⁡2132 ^ { \log _ { 2 } 13 }2log2​13

Write in exponential form. - 12=log⁡164\frac { 1 } { 2 } = \log _ { 16 } 421​=log16​4

Solve. - log⁡3x=−2\log _ { 3 } x = - 2log3​x=−2

Express as a sum of logarithms. - log⁡10xy\log _ { 10 } x ylog10​xy

Real Numbers and Variables

Equations, Inequalities, and Applications

Graphing and Functions

Systems of Linear Equations and Inequalities

Exponents and Polynomials

Factoring

Rational Expressions and Equations

Rational Exponents and Radicals

Quadratic Equations and Inequalities

The Conic Sections

Additional Properties of Functions

Filters

Solve. - $\log _ { a } 1000 = 3$

Graph the function. - $f ( x ) = e ^ { x - 1 }$ $Graph the function. - f ( x ) = e ^ { x - 1 }$

Write the expression as the sum or difference of single logarithms. - $\log _ { 10 } \left( \frac { \sqrt [ 3 ] { 17 } } { x ^ { 2 } y } \right)$

Evaluate. - $\log _ { 11 } 1$

Graph the function. - $f(x)=2^{x}$ $Graph the function. - f(x)=2^{x}$

Write in logarithmic form. - $\frac { 1 } { 16 } = 4 ^ { - 2 }$

Solve. - $\log _ { 25 } 5 = w$

Write in exponential form. - $0 = \log _ { 13 } 1$

Write in logarithmic form. - $343 = 7 ^ { 3 }$

Express as a sum of logarithms. - $\log _ { 4 } ( 5 \cdot 11 )$

Solve. - $\log _ { 4 } \frac { 1 } { 64 } = x$

Graph the function. - $f ( x ) = 4 ^ { - x }$ $Graph the function. - f ( x ) = 4 ^ { - x }$

Solve for x. - $4 ^ { - x } = \frac { 1 } { 16 }$

Evaluate. - $2 ^ { \log _ { 2 } 13 }$

Write in exponential form. - $\frac { 1 } { 2 } = \log _ { 16 } 4$

Solve. - $\log _ { 3 } x = - 2$

Express as a sum of logarithms. - $\log _ { 10 } x y$