Question 1

Express as a difference of logarithms.
-$\log _ { 10 } \left( \frac { C } { E } \right)$

Accepted Answer

A)  $\log C - \log E - \log 10$ 
B)  $\log ( C - E - 10 )$ 
C)  $\log _ { 5 } \mathrm { C } - \log _ { 5 } \mathrm { E }$ 
D)  $\log _ { 10 } C - \log _ { 10 } E$ 
A)  $\log C - \log E - \log 10$ 
B)  $\log ( C - E - 10 )$ 
C)  $\log _ { 5 } \mathrm { C } - \log _ { 5 } \mathrm { E }$ 
D)  $\log _ { 10 } C - \log _ { 10 } E$

Question 2

Solve for x.
-$$4 - 3 x + 5 = \frac { 1 } { 256 }$$

Accepted Answer

A)  $x = 128$ 
B)  $x = \frac { 1 } { 64 }$ 
C)  $x = 3$ 
D)  $x = - 3$ 
A)  $x = 128$ 
B)  $x = \frac { 1 } { 64 }$ 
C)  $x = 3$ 
D)  $x = - 3$

Question 3

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

Accepted Answer

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

Question 4

Write in exponential form.
-$$3 = \log _ { 5 } 125$$

Accepted Answer

A)  $5 ^ { 3 } = 125$ 
B)  $3 ^ { 5 } = 125$ 
C)  $125 ^ { 3 } = 5$ 
D)  $5 ^ { 125 } = 3$ 
A)  $5 ^ { 3 } = 125$ 
B)  $3 ^ { 5 } = 125$ 
C)  $125 ^ { 3 } = 5$ 
D)  $5 ^ { 125 } = 3$

Question 5

Express as a difference of logarithms.
-$\log _ { 7 } a ^ { 4 }$

Accepted Answer

A)  $\log ( 7 \cdot a \cdot 4 )$ 
B)  $\log _ { 7 } a \cdot \log _ { 7 } 4$ 
C)  $4 \log _ { 7 } a$ 
D)  $\log 7 \cdot \log a \cdot \log 4$ 
A)  $\log ( 7 \cdot a \cdot 4 )$ 
B)  $\log _ { 7 } a \cdot \log _ { 7 } 4$ 
C)  $4 \log _ { 7 } a$ 
D)  $\log 7 \cdot \log a \cdot \log 4$

Question 6

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
-A mixture has a pH of $6.3$. Find the concentration of hydrogen ions $\left[ \mathrm { H } ^ { + } \right]$in the mixture. Is the mixture an acid or a base?

Accepted Answer

A)  $10 ^ { 6.3 }$, base 
B)  $10 ^ { 6.3 }$, acid 
C)  $10 ^ { - 6.3 }$, acid 
D)  $10 ^ { - 6.3 }$, base 
A)  $10 ^ { 6.3 }$, base 
B)  $10 ^ { 6.3 }$, acid 
C)  $10 ^ { - 6.3 }$, acid 
D)  $10 ^ { - 6.3 }$, base

Question 7

Graph.
-$y=\log _{1 / 4^{x}}$

Accepted Answer

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

Question 8

Solve for x.
-$$y = 180 ( 2.7 ) ^ { 0.07 t }$$

Accepted Answer

A)  402 
B)  428 
C)  415 
D)  408 
A)  402 
B)  428 
C)  415 
D)  408

Question 9

Express as a sum of logarithms.
-$\log _ { 8 } 12 x$

Accepted Answer

A)  $\log _ { 4 } 12 + \log _ { 4 } x$ 
B)  $\log _ { 8 } 12 + \log _ { 8 } x$ 
C)  $\log _ { 4 } 12 - \log _ { 4 } x$ 
D)  $\log _ { 8 } 12 - \log _ { 8 } x$ 
A)  $\log _ { 4 } 12 + \log _ { 4 } x$ 
B)  $\log _ { 8 } 12 + \log _ { 8 } x$ 
C)  $\log _ { 4 } 12 - \log _ { 4 } x$ 
D)  $\log _ { 8 } 12 - \log _ { 8 } x$

Question 10

Write the expression as the sum or difference of single logarithms.
-$\log _ { 5 } \frac { \sqrt [ 4 ] { x } \sqrt [ 3 ] { y } } { z ^ { 2 } }$

Accepted Answer

A)  $\frac { 1 } { 4 } \log _ { 5 } x + \frac { 1 } { 3 } \log _ { 5 } y - 2 \log _ { 5 } z$ 
B)  $\frac { 4 } { 5 } \log _ { 5 } x + \frac { 3 } { 5 } \log _ { 5 } y - \frac { 2 } { 5 } \log _ { 5 } z$ 
C)  $\frac { 1 } { 4 } \log _ { 5 } x \cdot \frac { 1 } { 3 } \log _ { 5 } y \div 2 \log _ { 5 } z$ 
D)  $4 \log _ { 5 } x + 3 \log _ { 5 } y - 2 \log _ { 5 } z$ 
A)  $\frac { 1 } { 4 } \log _ { 5 } x + \frac { 1 } { 3 } \log _ { 5 } y - 2 \log _ { 5 } z$ 
B)  $\frac { 4 } { 5 } \log _ { 5 } x + \frac { 3 } { 5 } \log _ { 5 } y - \frac { 2 } { 5 } \log _ { 5 } z$ 
C)  $\frac { 1 } { 4 } \log _ { 5 } x \cdot \frac { 1 } { 3 } \log _ { 5 } y \div 2 \log _ { 5 } z$ 
D)  $4 \log _ { 5 } x + 3 \log _ { 5 } y - 2 \log _ { 5 } z$

Question 11

Solve for x.
-$$2 ^ { 3 x + 7 } = \frac { 1 } { 4 }$$

Accepted Answer

A)  $x = 1$ 
B)  $x = \frac { 1 } { 2 }$ 
C)  $x = - 3$ 
D)  $x = 3$ 
A)  $x = 1$ 
B)  $x = \frac { 1 } { 2 }$ 
C)  $x = - 3$ 
D)  $x = 3$

Question 12

Evaluate.
-$$\log _ { 10 } 100$$

Accepted Answer

A)  $x = - 2$ 
B)  $x = 2$ 
C)  $x = 20$ 
D)  $x = \frac { 1 } { 100 }$ 
A)  $x = - 2$ 
B)  $x = 2$ 
C)  $x = 20$ 
D)  $x = \frac { 1 } { 100 }$

Question 13

Graph.
-$y=\log _{2} x$

Accepted Answer

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

Question 14

Solve.
-$$\log _ { 9 } x = 1$$

Accepted Answer

A)  $x = 9$ 
B)  $x = \frac { 1 } { 9 }$ 
C)  $x = 1$ 
D)  $x = 0$ 
A)  $x = 9$ 
B)  $x = \frac { 1 } { 9 }$ 
C)  $x = 1$ 
D)  $x = 0$

Question 15

Graph the function.
-$$f ( x ) = e ^ { 6 x }$$

Accepted Answer

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

Question 16

Express as a product.
-$\log _ { 9 } B ^ { - 2 }$

Accepted Answer

A)  $- \log _ { 9 }$ B $\cdot \log _ { 9 } 2$ 
B)  $- \log 9 \cdot \log B \cdot \log 2$ 
C)  $\log ( 9 \cdot B \cdot - 2 )$ 
D)  $- 2 \log _ { 9 } B$ 
A)  $- \log _ { 9 }$ B $\cdot \log _ { 9 } 2$ 
B)  $- \log 9 \cdot \log B \cdot \log 2$ 
C)  $\log ( 9 \cdot B \cdot - 2 )$ 
D)  $- 2 \log _ { 9 } B$

Question 17

Graph the function.
-$(x)=4^{x-3}$

Accepted Answer

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

Question 18

Write in logarithmic form.
-$$0.001 = 10 ^ { - 3 }$$

Accepted Answer

A)  $\log _ { - 3 } 10 = 0.001$ 
B)  $\log _ { 10 } ( - 3 ) = 0.001$ 
C)  $\log _ { 10 } ( 0.001 ) = - 3$ 
D)  $\log _ { - 3 } ( 0.001 ) = 10$ 
A)  $\log _ { - 3 } 10 = 0.001$ 
B)  $\log _ { 10 } ( - 3 ) = 0.001$ 
C)  $\log _ { 10 } ( 0.001 ) = - 3$ 
D)  $\log _ { - 3 } ( 0.001 ) = 10$

Question 19

Write in exponential form.
-$$- 3 = \log _ { 2 } \frac { 1 } { 8 }$$

Accepted Answer

A)  $2 ^ { 8 } = 3$ 
B)  $2 ^ { - 3 } = \frac { 1 } { 8 }$ 
C)  $\left( \frac { 1 } { 8 } \right) ^ { 3 } = 2$ 
D)  $3 ^ { 2 } = \frac { 1 } { 8 }$ 
A)  $2 ^ { 8 } = 3$ 
B)  $2 ^ { - 3 } = \frac { 1 } { 8 }$ 
C)  $\left( \frac { 1 } { 8 } \right) ^ { 3 } = 2$ 
D)  $3 ^ { 2 } = \frac { 1 } { 8 }$

Question 20

Express as a product.
-$\log _ { 6 } \sqrt { z }$

Accepted Answer

A)  $\frac { 1 } { 2 } \log ( 6 \cdot z )$ 
B)  $\frac { 1 } { 2 } \log 6 + \frac { 1 } { 2 } \log z$ 
C)  $\frac { 1 } { 2 } \log _ { 6 } z$ 
D)  $\frac { 1 } { 2 } \log 6 \cdot \log z$ 
A)  $\frac { 1 } { 2 } \log ( 6 \cdot z )$ 
B)  $\frac { 1 } { 2 } \log 6 + \frac { 1 } { 2 } \log z$ 
C)  $\frac { 1 } { 2 } \log _ { 6 } z$ 
D)  $\frac { 1 } { 2 } \log 6 \cdot \log z$

Express as a difference of logarithms. - $\log _ { 10 } \left( \frac { C } { E } \right)$

Solve for x. - $4 - 3 x + 5 = \frac { 1 } { 256 }$

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

Write in exponential form. - $3 = \log _ { 5 } 125$

Express as a difference of logarithms. - $\log _ { 7 } a ^ { 4 }$

Graph. - $y=\log _{1 / 4^{x}}$ $Graph. - y=\log _{1 / 4^{x}}$

Solve for x. - $y = 180 ( 2.7 ) ^ { 0.07 t }$

Express as a sum of logarithms. - $\log _ { 8 } 12 x$

Write the expression as the sum or difference of single logarithms. - $\log _ { 5 } \frac { \sqrt [ 4 ] { x } \sqrt [ 3 ] { y } } { z ^ { 2 } }$

Solve for x. - $2 ^ { 3 x + 7 } = \frac { 1 } { 4 }$

Evaluate. - $\log _ { 10 } 100$

Graph. - $y=\log _{2} x$ $Graph. - y=\log _{2} x$

Solve. - $\log _ { 9 } x = 1$

Graph the function. - $f ( x ) = e ^ { 6 x }$ $Graph the function. - f ( x ) = e ^ { 6 x }$

Express as a product. - $\log _ { 9 } B ^ { - 2 }$

Graph the function. - $(x)=4^{x-3}$ $Graph the function. - (x)=4^{x-3}$

Write in logarithmic form. - $0.001 = 10 ^ { - 3 }$

Write in exponential form. - $- 3 = \log _ { 2 } \frac { 1 } { 8 }$

Express as a product. - $\log _ { 6 } \sqrt { z }$

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

Express as a difference of logarithms. - log⁡10(CE)\log _ { 10 } \left( \frac { C } { E } \right)log10​(EC​)

Solve for x. - 4−3x+5=12564 - 3 x + 5 = \frac { 1 } { 256 }4−3x+5=2561​

Solve for x. - 3x=13 ^ { x } = 13x=1

Write in exponential form. - 3=log⁡51253 = \log _ { 5 } 1253=log5​125

Express as a difference of logarithms. - log⁡7a4\log _ { 7 } a ^ { 4 }log7​a4

Graph. - y=log⁡1/4xy=\log _{1 / 4^{x}}y=log1/4x​

Solve for x. - y=180(2.7)0.07ty = 180 ( 2.7 ) ^ { 0.07 t }y=180(2.7)0.07t

Express as a sum of logarithms. - log⁡812x\log _ { 8 } 12 xlog8​12x

Write the expression as the sum or difference of single logarithms. - log⁡5x4y3z2\log _ { 5 } \frac { \sqrt [ 4 ] { x } \sqrt [ 3 ] { y } } { z ^ { 2 } }log5​z24x​3y​​

Solve for x. - 23x+7=142 ^ { 3 x + 7 } = \frac { 1 } { 4 }23x+7=41​

Evaluate. - log⁡10100\log _ { 10 } 100log10​100

Graph. - y=log⁡2xy=\log _{2} xy=log2​x

Solve. - log⁡9x=1\log _ { 9 } x = 1log9​x=1

Graph the function. - f(x)=e6xf ( x ) = e ^ { 6 x }f(x)=e6x

Express as a product. - log⁡9B−2\log _ { 9 } B ^ { - 2 }log9​B−2

Graph the function. - (x)=4x−3(x)=4^{x-3}(x)=4x−3

Write in logarithmic form. - 0.001=10−30.001 = 10 ^ { - 3 }0.001=10−3

Write in exponential form. - −3=log⁡218- 3 = \log _ { 2 } \frac { 1 } { 8 }−3=log2​81​

Express as a product. - log⁡6z\log _ { 6 } \sqrt { z }log6​z​

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

Express as a difference of logarithms. - $\log _ { 10 } \left( \frac { C } { E } \right)$

Solve for x. - $4 - 3 x + 5 = \frac { 1 } { 256 }$

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

Write in exponential form. - $3 = \log _ { 5 } 125$

Express as a difference of logarithms. - $\log _ { 7 } a ^ { 4 }$

Graph. - $y=\log _{1 / 4^{x}}$ $Graph. - y=\log _{1 / 4^{x}}$

Solve for x. - $y = 180 ( 2.7 ) ^ { 0.07 t }$

Express as a sum of logarithms. - $\log _ { 8 } 12 x$

Write the expression as the sum or difference of single logarithms. - $\log _ { 5 } \frac { \sqrt [ 4 ] { x } \sqrt [ 3 ] { y } } { z ^ { 2 } }$

Solve for x. - $2 ^ { 3 x + 7 } = \frac { 1 } { 4 }$

Evaluate. - $\log _ { 10 } 100$

Graph. - $y=\log _{2} x$ $Graph. - y=\log _{2} x$

Solve. - $\log _ { 9 } x = 1$

Graph the function. - $f ( x ) = e ^ { 6 x }$ $Graph the function. - f ( x ) = e ^ { 6 x }$

Express as a product. - $\log _ { 9 } B ^ { - 2 }$

Graph the function. - $(x)=4^{x-3}$ $Graph the function. - (x)=4^{x-3}$

Write in logarithmic form. - $0.001 = 10 ^ { - 3 }$

Write in exponential form. - $- 3 = \log _ { 2 } \frac { 1 } { 8 }$

Express as a product. - $\log _ { 6 } \sqrt { z }$