Question 1

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

Accepted Answer

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

Question 2

Write the expression as the sum or difference of single logarithms.
-$\log _ { 13 } \sqrt { \frac { x y } { 5 } }$

Accepted Answer

A)  $\frac { 1 } { 2 } \log _ { 13 } x + \frac { 1 } { 2 } \log _ { 13 } y - \log _ { 13 } 5$ 
B)  $\frac { 1 } { 2 } \log _ { 13 } x \cdot \frac { 1 } { 2 } \log _ { 13 } y + \frac { 1 } { 2 } \log _ { 13 } 5$ 
C)  $\frac { 1 } { 2 } \log _ { 13 } x + \frac { 1 } { 2 } \log _ { 13 } y - \frac { 1 } { 2 } \log _ { 13 } 5$ 
D)  $\frac { 1 } { 2 } \log _ { 13 } x y - \frac { 1 } { 2 } \log _ { 13 } 5$ 
A)  $\frac { 1 } { 2 } \log _ { 13 } x + \frac { 1 } { 2 } \log _ { 13 } y - \log _ { 13 } 5$ 
B)  $\frac { 1 } { 2 } \log _ { 13 } x \cdot \frac { 1 } { 2 } \log _ { 13 } y + \frac { 1 } { 2 } \log _ { 13 } 5$ 
C)  $\frac { 1 } { 2 } \log _ { 13 } x + \frac { 1 } { 2 } \log _ { 13 } y - \frac { 1 } { 2 } \log _ { 13 } 5$ 
D)  $\frac { 1 } { 2 } \log _ { 13 } x y - \frac { 1 } { 2 } \log _ { 13 } 5$ C

Question 3

Express as a difference of logarithms.
-$\log _ { 6 } \left( \frac { 15 } { F } \right)$

Accepted Answer

A)  $\log ( 15 - \mathrm { F } - 6 )$ 
B)  $\log _ { 3 } 15 - \log _ { 3 } \mathrm {~F}$ 
C)  $\log _ { 6 } 15 - \log _ { 6 } F$ 
D)  $\log 15 - \log F - \log 6$ 
A)  $\log ( 15 - \mathrm { F } - 6 )$ 
B)  $\log _ { 3 } 15 - \log _ { 3 } \mathrm {~F}$ 
C)  $\log _ { 6 } 15 - \log _ { 6 } F$ 
D)  $\log 15 - \log F - \log 6$ D

Question 4

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

Accepted Answer

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

Question 5

Evaluate.
-$\log _ { 7 } 7$

Accepted Answer

A)  $x = \frac { 1 } { 7 }$ 
B)  $x = 1$ 
C)  $x = 0$ 
D)  $x = 7$ 
A)  $x = \frac { 1 } { 7 }$ 
B)  $x = 1$ 
C)  $x = 0$ 
D)  $x = 7$

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

Accepted Answer

A)  $10 ^ { 7.6 }$, base 
B)  $10 ^ { - 7.6 }$, base 
C)  $10 ^ { 7.6 }$, acid 
D)  $10 ^ { - 7.6 }$, acid 
A)  $10 ^ { 7.6 }$, base 
B)  $10 ^ { - 7.6 }$, base 
C)  $10 ^ { 7.6 }$, acid 
D)  $10 ^ { - 7.6 }$, acid

Question 7

Write the expression as the sum or difference of single logarithms.
-$\log _ { 9 } \left( \frac { 8 \sqrt { x } } { y } \right)$

Accepted Answer

A)  $\log _ { 9 } 8 \cdot \frac { 1 } { 2 } \log _ { 9 } m \div \log _ { 9 } y$ 
B)  $\log _ { 9 } 8 + \frac { 1 } { 2 } \log _ { 9 } x - \log _ { 9 } y$ 
C)  $\log _ { 9 } ( 8 \sqrt { x } ) - \log _ { 9 } y$ 
D)  $\log _ { 9 } y - \log _ { 9 } 8 - \frac { 1 } { 2 } \log _ { 9 } x$ 
A)  $\log _ { 9 } 8 \cdot \frac { 1 } { 2 } \log _ { 9 } m \div \log _ { 9 } y$ 
B)  $\log _ { 9 } 8 + \frac { 1 } { 2 } \log _ { 9 } x - \log _ { 9 } y$ 
C)  $\log _ { 9 } ( 8 \sqrt { x } ) - \log _ { 9 } y$ 
D)  $\log _ { 9 } y - \log _ { 9 } 8 - \frac { 1 } { 2 } \log _ { 9 } x$

Question 8

Solve for x.
-$$4 - 2 x + 10 = 256$$

Accepted Answer

A)  $x = 5$ 
B)  $x = 3$ 
C)  $x = 64$ 
D)  $x = - 3$ 
A)  $x = 5$ 
B)  $x = 3$ 
C)  $x = 64$ 
D)  $x = - 3$

Question 9

Solve for x.
-$$5 ^ { x } = \frac { 1 } { 25 }$$

Accepted Answer

A)  $x = \frac { 1 } { 5 }$ 
B)  $x = - 2$ 
C)  $x = \frac { 1 } { 2 }$ 
D)  $x = 2$ 
A)  $x = \frac { 1 } { 5 }$ 
B)  $x = - 2$ 
C)  $x = \frac { 1 } { 2 }$ 
D)  $x = 2$

Question 10

Evaluate.
-$\log _ { 64 } 4$

Accepted Answer

A)  $x = 1$ 
B)  $x = \frac { 1 } { 2 }$ 
C)  $x = 12$ 
D)  $x = 3$ 
A)  $x = 1$ 
B)  $x = \frac { 1 } { 2 }$ 
C)  $x = 12$ 
D)  $x = 3$

Question 11

Graph the function.
-

Accepted Answer

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

Question 12

Solve.
-$\log _ { 6 } \left( \frac { 1 } { 36 } \right) = y$

Accepted Answer

A)  $y = - 2$ 
B)  $y = 2$ 
C)  $y = - 36$ 
D)  $y = 6$ 
A)  $y = - 2$ 
B)  $y = 2$ 
C)  $y = - 36$ 
D)  $y = 6$

Question 13

Solve for x.
-A city is growing at the rate of $0.3 \%$ annually. If there were $5,226,000$ residents in the city in 2008 , find how many (to the nearest ten-thousand) are living in that city in 2012 . Use $y = 5,226,000 ( 2.7 ) ^ { 0.003 t }$.

Accepted Answer

A)  $5,290,000$ 
B)  $5,320,000$ 
C)  $14,110,000$ 
D)  170,000 
A)  $5,290,000$ 
B)  $5,320,000$ 
C)  $14,110,000$ 
D)  170,000

Question 14

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

Accepted Answer

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

Question 15

Solve for x.
-$$2 ^ { x } = 16$$

Accepted Answer

A)  $x = 5$ 
B)  $x = 8$ 
C)  $x = 4$ 
D)  $x = 3$ 
A)  $x = 5$ 
B)  $x = 8$ 
C)  $x = 4$ 
D)  $x = 3$

Question 16

Write in logarithmic form.
-$$\frac { 1 } { 196 } = 14 ^ { - 2 }$$

Accepted Answer

A)  $\log _ { 14 } \frac { 1 } { 196 } = - 2$ 
B)  $\log _ { 14 } \frac { 1 } { 196 } = 14$ 
C)  $\log _ { 14 } ( - 2 ) = \frac { 1 } { 196 }$ 
D)  $\log \frac { 1 } { 196 } 14 = - 2$ 
A)  $\log _ { 14 } \frac { 1 } { 196 } = - 2$ 
B)  $\log _ { 14 } \frac { 1 } { 196 } = 14$ 
C)  $\log _ { 14 } ( - 2 ) = \frac { 1 } { 196 }$ 
D)  $\log \frac { 1 } { 196 } 14 = - 2$

Question 17

Express as a product.
-$\log _ { 4 } \frac { 13 } { 11 }$

Accepted Answer

A)  $\log _ { 2 } 13 - \log _ { 2 } 11$ 
B)  $\log _ { 4 } 13 - \log _ { 4 } 11$ 
C)  $\log _ { 4 } 11 - \log _ { 4 } 13$ 
D)  $\log _ { 4 } 13 + \log _ { 4 } 11$ 
A)  $\log _ { 2 } 13 - \log _ { 2 } 11$ 
B)  $\log _ { 4 } 13 - \log _ { 4 } 11$ 
C)  $\log _ { 4 } 11 - \log _ { 4 } 13$ 
D)  $\log _ { 4 } 13 + \log _ { 4 } 11$

Question 18

Solve.
-$$\log _ { x } 125 = 3$$

Accepted Answer

A)  $x = - 5$ 
B)  $x = - 3$ 
C)  $x = \frac { 1 } { 125 }$ 
D)  $x = 5$ 
A)  $x = - 5$ 
B)  $x = - 3$ 
C)  $x = \frac { 1 } { 125 }$ 
D)  $x = 5$

Question 19

Write in logarithmic form.
-$$8 = 2 ^ { 3 }$$

Accepted Answer

A)  $\log _ { 8 } 2 = 3$ 
B)  $\log _ { 2 } 3 = 8$ 
C)  $\log _ { 3 } 8 = 2$ 
D)  $\log _ { 2 } 8 = 3$ 
A)  $\log _ { 8 } 2 = 3$ 
B)  $\log _ { 2 } 3 = 8$ 
C)  $\log _ { 3 } 8 = 2$ 
D)  $\log _ { 2 } 8 = 3$

Question 20

Solve.
-$$\log _ { 7 } 1 = x$$

Accepted Answer

A)  $x = 0$ 
B)  $x = 7$ 
C)  $x = 1$ 
D)  $x = 49$ 
A)  $x = 0$ 
B)  $x = 7$ 
C)  $x = 1$ 
D)  $x = 49$

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

Write the expression as the sum or difference of single logarithms. - $\log _ { 13 } \sqrt { \frac { x y } { 5 } }$

Express as a difference of logarithms. - $\log _ { 6 } \left( \frac { 15 } { F } \right)$

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

Evaluate. - $\log _ { 7 } 7$

Write the expression as the sum or difference of single logarithms. - $\log _ { 9 } \left( \frac { 8 \sqrt { x } } { y } \right)$

Solve for x. - $4 - 2 x + 10 = 256$

Solve for x. - $5 ^ { x } = \frac { 1 } { 25 }$

Evaluate. - $\log _ { 64 } 4$

Graph the function. -

Solve. - $\log _ { 6 } \left( \frac { 1 } { 36 } \right) = y$

Solve for x. -A city is growing at the rate of $0.3 \%$ annually. If there were $5,226,000$ residents in the city in 2008 , find how many (to the nearest ten-thousand) are living in that city in 2012 . Use $y = 5,226,000 ( 2.7 ) ^ { 0.003 t }$ .

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

Solve for x. - $2 ^ { x } = 16$

Write in logarithmic form. - $\frac { 1 } { 196 } = 14 ^ { - 2 }$

Express as a product. - $\log _ { 4 } \frac { 13 } { 11 }$

Solve. - $\log _ { x } 125 = 3$

Write in logarithmic form. - $8 = 2 ^ { 3 }$

Solve. - $\log _ { 7 } 1 = x$

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

Evaluate. - log⁡55\log _ { 5 } \sqrt { 5 }log5​5​

Write the expression as the sum or difference of single logarithms. - log⁡13xy5\log _ { 13 } \sqrt { \frac { x y } { 5 } }log13​5xy​​

Express as a difference of logarithms. - log⁡6(15F)\log _ { 6 } \left( \frac { 15 } { F } \right)log6​(F15​)

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

Evaluate. - log⁡77\log _ { 7 } 7log7​7

Write the expression as the sum or difference of single logarithms. - log⁡9(8xy)\log _ { 9 } \left( \frac { 8 \sqrt { x } } { y } \right)log9​(y8x​​)

Solve for x. - 4−2x+10=2564 - 2 x + 10 = 2564−2x+10=256

Solve for x. - 5x=1255 ^ { x } = \frac { 1 } { 25 }5x=251​

Evaluate. - log⁡644\log _ { 64 } 4log64​4