Question 1

Write in exponential form.
-$$- 6 = \log _ { 10 } ( 0.000001 )$$

Accepted Answer

A)  $0.000001 ^ { - 6 } = 10$ 
B)  $10 ^ { - 6 } = 0.000001$ 
C)  $0.000001 ^ { 10 } = - 6$ 
D)  $- 6^{10} = 0.000001$ 
A)  $0.000001 ^ { - 6 } = 10$ 
B)  $10 ^ { - 6 } = 0.000001$ 
C)  $0.000001 ^ { 10 } = - 6$ 
D)  $- 6^{10} = 0.000001$

Question 2

Solve for x.
-$$3 ^ { 2 x + 1 } = 27$$

Accepted Answer

A)  $x = - 1$ 
B)  $x = 9$ 
C)  $x = 3$ 
D)  $x = 1$ 
A)  $x = - 1$ 
B)  $x = 9$ 
C)  $x = 3$ 
D)  $x = 1$

Question 3

Write in logarithmic form.
-$$\mathrm { y } = \mathrm { e } ^ { - 2 }$$

Accepted Answer

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

Question 4

Graph.
-On a coordinate plane, graph the function $\mathrm { f }$ and the function $\mathrm { f } ^ { - 1 }$. Then graph a dashed line for the equation $\mathrm { y } =$
$$f ( x ) = \log _ { 5 } x , f ^ { - 1 } ( x ) = 5 ^ { x }$$

Accepted Answer

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

Question 5

Write in exponential form.
-$$\text { -3 = } \log _ { 10 } 0.001$$

Accepted Answer

A)  $100.001 = - 3$ 
B)  $0.001 ^ { - 3 } = 10$ 
C)  $- 3^{10} = 0.001$ 
D)  $10 ^ { - 3 } = 0.001$ 
A)  $100.001 = - 3$ 
B)  $0.001 ^ { - 3 } = 10$ 
C)  $- 3^{10} = 0.001$ 
D)  $10 ^ { - 3 } = 0.001$

Question 6

Evaluate.
-$\log _ { 5 } \sqrt [ 6 ] { 5 }$

Accepted Answer

A)  $x = 15,625$ 
B)  $x = \frac { 1 } { 6 }$ 
C)  $x = 6$ 
D)  $x = \frac { 1 } { 15,625 }$ 
A)  $x = 15,625$ 
B)  $x = \frac { 1 } { 6 }$ 
C)  $x = 6$ 
D)  $x = \frac { 1 } { 15,625 }$

Question 7

Solve for x.
-The number of bacteria in a culture is given by $B ( t ) = 8000 \left( 2 ^ { t } \right)$, where $t$ is the time in hours. How many bacteria will grow in the culture in the first 8 hours?

Accepted Answer

A)  $2,048,000$ 
B)  224,000 
C)  128,000 
D)  80,000 
A)  $2,048,000$ 
B)  224,000 
C)  128,000 
D)  80,000

Question 8

Solve for x.
-The radioactive decay of radon 222 can be described by the equation $\mathrm { A } = \mathrm { Ce } \mathrm { e } ^ { - 0.1813 \mathrm { t } }$, where $\mathrm { C }$ is the original amount of radon and $\mathrm { A }$ is the amount of radon after $\mathrm { t }$ days. If $2.5$ milligrams are in a laboratory container today, how much was there is the container 11 days ago? Round to the nearest hundredth.

Accepted Answer

A)  $2.84 \mathrm { mg }$ 
B)  $0.34 \mathrm { mg }$ 
C)  $45.68 \mathrm { mg }$ 
D)  $18.37 \mathrm { mg }$ 
A)  $2.84 \mathrm { mg }$ 
B)  $0.34 \mathrm { mg }$ 
C)  $45.68 \mathrm { mg }$ 
D)  $18.37 \mathrm { mg }$

Question 9

Evaluate.
-$\log _ { 5 } 125$

Accepted Answer

A)  $x = 3$ 
B)  $x = \frac { 1 } { 3 }$ 
C)  $x = 1$ 
D)  $x = 15$ 
A)  $x = 3$ 
B)  $x = \frac { 1 } { 3 }$ 
C)  $x = 1$ 
D)  $x = 15$

Question 10

Solve for x.
-Mary is investing $\$ 8000$ at an annual rate of $5.4 \%$ compounded annually. How much money will Mary have after 6 years? Use the interest formula $A = P \left( 1 + \frac { r } { n } \right) ^ { n t }$. Round the answer to the nearest cent.

Accepted Answer

A)  $\$ 50,592.00$ 
B)  $\$ 10,592.00$ 
C)  $\$ 106,712.26$ 
D)  $\$ 10,968.16$ 
A)  $\$ 50,592.00$ 
B)  $\$ 10,592.00$ 
C)  $\$ 106,712.26$ 
D)  $\$ 10,968.16$

Question 11

Evaluate.
-$\log _ { 10 } ( 0.01 )$

Accepted Answer

A)  $x = - 20$ 
B)  $x = 100$ 
C)  $x = 2$ 
D)  $x = - 2$ 
A)  $x = - 20$ 
B)  $x = 100$ 
C)  $x = 2$ 
D)  $x = - 2$

Question 12

Evaluate.
-$\log _ { 3 } \frac { 1 } { 9 }$

Accepted Answer

A)  $x = - 2$ 
B)  $x = 6$ 
C)  $x = 2$ 
D)  $x = \frac { 1 } { 2 }$ 
A)  $x = - 2$ 
B)  $x = 6$ 
C)  $x = 2$ 
D)  $x = \frac { 1 } { 2 }$

Question 13

Write in logarithmic form.
-$$100,000 = 10 ^ { 5 }$$

Accepted Answer

A)  $\log _ { 5 } 100,000 = 10$ 
B)  $\log _ { 10 } 100,000 = 5$ 
C)  $\log _ { 5 } 10 = 100,000$ 
D)  $\log _ { 10 } 5 = 100,000$ 
A)  $\log _ { 5 } 100,000 = 10$ 
B)  $\log _ { 10 } 100,000 = 5$ 
C)  $\log _ { 5 } 10 = 100,000$ 
D)  $\log _ { 10 } 5 = 100,000$

Question 14

Solve for x.
-$$4 x - 1 = 1024$$

Accepted Answer

A)  $x = 4$ 
B)  $x = 2$ 
C)  $x = 1$ 
D)  $x = 3$ 
A)  $x = 4$ 
B)  $x = 2$ 
C)  $x = 1$ 
D)  $x = 3$

Question 15

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 $10 ^ { - 9.7 }$. What is the pH of the solution? Is the solution an acid or a base?

Accepted Answer

A)  The $\mathrm { pH }$ is 9.7. The solution is a base. 
B)  The $\mathrm { pH }$ is 9.7. The solution is an acid. 
C)  The $\mathrm { pH }$ is $- 9.7$. The solution is a base. 
D)  The $\mathrm { pH }$ is $- 9.7$. The solution is an acid. 
A)  The $\mathrm { pH }$ is 9.7. The solution is a base. 
B)  The $\mathrm { pH }$ is 9.7. The solution is an acid. 
C)  The $\mathrm { pH }$ is $- 9.7$. The solution is a base. 
D)  The $\mathrm { pH }$ is $- 9.7$. The solution is an acid.

Question 16

Solve.
-$$\frac { 3 } { 7 } = \log _ { e } x$$

Accepted Answer

A)  $e ^ { 3 / 7 } = x$ 
B)  $\mathrm { e } ^ { \mathrm { x } } = \frac { 3 } { 7 }$ 
C)  $x ^ { e } = \frac { 3 } { 7 }$ 
D)  $x ^ { 3 / 7 } = e$ 
A)  $e ^ { 3 / 7 } = x$ 
B)  $\mathrm { e } ^ { \mathrm { x } } = \frac { 3 } { 7 }$ 
C)  $x ^ { e } = \frac { 3 } { 7 }$ 
D)  $x ^ { 3 / 7 } = e$

Question 17

Solve.
-$$\log _ { 5 } x = 3$$

Accepted Answer

A)  $x = 125$ 
B)  $x = 8$ 
C)  $x = 243$ 
D)  $x = 15$ 
A)  $x = 125$ 
B)  $x = 8$ 
C)  $x = 243$ 
D)  $x = 15$

Question 18

Graph the function.
-$$f ( x ) = 4 ^ { x } + 2$$

Accepted Answer

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

Question 19

Write in exponential form.
-$$\log _ { 3 } 9 = x$$

Accepted Answer

A)  $x = 2$ 
B)  $x = 27$ 
C)  $x = 12$ 
D)  $x = 3$ 
A)  $x = 2$ 
B)  $x = 27$ 
C)  $x = 12$ 
D)  $x = 3$

Write in exponential form. - $- 6 = \log _ { 10 } ( 0.000001 )$

Solve for x. - $3 ^ { 2 x + 1 } = 27$

Write in logarithmic form. - $\mathrm { y } = \mathrm { e } ^ { - 2 }$

Write in exponential form. - $\text { -3 = } \log _ { 10 } 0.001$

Evaluate. - $\log _ { 5 } \sqrt [ 6 ] { 5 }$

Solve for x. -The number of bacteria in a culture is given by $B ( t ) = 8000 \left( 2 ^ { t } \right)$ , where $t$ is the time in hours. How many bacteria will grow in the culture in the first 8 hours?

Evaluate. - $\log _ { 5 } 125$

Solve for x. -Mary is investing $\$ 8000$ at an annual rate of $5.4 \%$ compounded annually. How much money will Mary have after 6 years? Use the interest formula $A = P \left( 1 + \frac { r } { n } \right) ^ { n t }$ . Round the answer to the nearest cent.

Evaluate. - $\log _ { 10 } ( 0.01 )$

Evaluate. - $\log _ { 3 } \frac { 1 } { 9 }$

Write in logarithmic form. - $100,000 = 10 ^ { 5 }$

Solve for x. - $4 x - 1 = 1024$

Solve. - $\frac { 3 } { 7 } = \log _ { e } x$

Solve. - $\log _ { 5 } x = 3$

Graph the function. - $f ( x ) = 4 ^ { x } + 2$ $Graph the function. - f ( x ) = 4 ^ { x } + 2$

Write in exponential form. - $\log _ { 3 } 9 = x$

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

Write in exponential form. - −6=log⁡10(0.000001)- 6 = \log _ { 10 } ( 0.000001 )−6=log10​(0.000001)

Solve for x. - 32x+1=273 ^ { 2 x + 1 } = 2732x+1=27

Write in logarithmic form. - y=e−2\mathrm { y } = \mathrm { e } ^ { - 2 }y=e−2

Graph. -On a coordinate plane, graph the function f\mathrm { f }f and the function f−1\mathrm { f } ^ { - 1 }f−1 . Then graph a dashed line for the equation y=\mathrm { y } =y= f(x)=log⁡5x,f−1(x)=5xf ( x ) = \log _ { 5 } x , f ^ { - 1 } ( x ) = 5 ^ { x }f(x)=log5​x,f−1(x)=5x

Write in exponential form. - -3 = log⁡100.001\text { -3 = } \log _ { 10 } 0.001 -3 = log10​0.001

Evaluate. - log⁡556\log _ { 5 } \sqrt [ 6 ] { 5 }log5​65​

Solve for x. -The number of bacteria in a culture is given by B(t)=8000(2t)B ( t ) = 8000 \left( 2 ^ { t } \right)B(t)=8000(2t) , where ttt is the time in hours. How many bacteria will grow in the culture in the first 8 hours?

Evaluate. - log⁡5125\log _ { 5 } 125log5​125

Solve for x. -Mary is investing $8000\$ 8000$8000 at an annual rate of 5.4%5.4 \%5.4% compounded annually. How much money will Mary have after 6 years? Use the interest formula A=P(1+rn)ntA = P \left( 1 + \frac { r } { n } \right) ^ { n t }A=P(1+nr​)nt . Round the answer to the nearest cent.

Evaluate. - log⁡10(0.01)\log _ { 10 } ( 0.01 )log10​(0.01)

Evaluate. - log⁡319\log _ { 3 } \frac { 1 } { 9 }log3​91​

Write in logarithmic form. - 100,000=105100,000 = 10 ^ { 5 }100,000=105

Solve for x. - 4x−1=10244 x - 1 = 10244x−1=1024

Solve. - 37=log⁡ex\frac { 3 } { 7 } = \log _ { e } x73​=loge​x

Solve. - log⁡5x=3\log _ { 5 } x = 3log5​x=3

Graph the function. - f(x)=4x+2f ( x ) = 4 ^ { x } + 2f(x)=4x+2

Write in exponential form. - log⁡39=x\log _ { 3 } 9 = xlog3​9=x