Question 1

Find the unknown value.
-$\log _ { 4 } \frac { 1 } { 64 } = y$

Accepted Answer

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

Question 2

Write the equation in logarithmic form.
-$25 ^ { - 1 / 2 } = \frac { 1 } { 5 }$

Accepted Answer

A)  $\log _ { - 1 / 2 } 25 = \frac { 1 } { 5 }$ 
B)  $\log _ { 1 / 5 } 25 = - \frac { 1 } { 2 }$ 
C)  $\log _ { 25 } \left( - \frac { 1 } { 2 } \right) = \frac { 1 } { 5 }$ 
D)  $\log _ { 25 } \left( \frac { 1 } { 5 } \right) = - \frac { 1 } { 2 }$ 
A)  $\log _ { - 1 / 2 } 25 = \frac { 1 } { 5 }$ 
B)  $\log _ { 1 / 5 } 25 = - \frac { 1 } { 2 }$ 
C)  $\log _ { 25 } \left( - \frac { 1 } { 2 } \right) = \frac { 1 } { 5 }$ 
D)  $\log _ { 25 } \left( \frac { 1 } { 5 } \right) = - \frac { 1 } { 2 }$

Question 3

Write the equation in logarithmic form.
-$$\mathrm { a } ^ { \mathrm { b } } = \mathrm { q }$$

Accepted Answer

A) loga b = q 
B) logq b = a 
C) logq a = b 
D) loga q = b 
A) loga b = q 
B) logq b = a 
C) logq a = b 
D) loga q = b

Question 4

To what exponent must the base 10 be raised to obtain the given value? Round the answer to four decimal places.
-0.0691

Accepted Answer

A) -1.1669 
B) -1.1543 
C) -1.1605 
D) -2.6722 
A) -1.1669 
B) -1.1543 
C) -1.1605 
D) -2.6722

Question 5

Use properties of logarithms to expand the logarithmic expression as much as possible.
-$\log _ { 7 } x ^ { 2 } ( x - 7 )$

Accepted Answer

A)  $2 \left( \log _ { 7 } x \right) ( \log _7 ( x - 7 ) )$ 
B)  $\log _ { 7 } 2 x + \log _7 ( 2 x - 14 )$ 
C)  $\log _ { 7 } \left( x ^ { 3 } + 49 x \right)$ 
D)  $2 \log _7 x + \log _7 ( x - 7 )$ 
A)  $2 \left( \log _ { 7 } x \right) ( \log _7 ( x - 7 ) )$ 
B)  $\log _ { 7 } 2 x + \log _7 ( 2 x - 14 )$ 
C)  $\log _ { 7 } \left( x ^ { 3 } + 49 x \right)$ 
D)  $2 \log _7 x + \log _7 ( x - 7 )$

Question 6

Use properties of logarithms to expand the logarithmic expression as much as possible.
-$\log _ { 8 } x ^ { 3 }$

Accepted Answer

A)  $3 \log _ { 8 } x ^ { 3 }$ 
B)  $3 \log _ { 8 } x$ 
C)  $8 \log _ { 3 } x$ 
D)  $8 \log x$ 
A)  $3 \log _ { 8 } x ^ { 3 }$ 
B)  $3 \log _ { 8 } x$ 
C)  $8 \log _ { 3 } x$ 
D)  $8 \log x$

Question 7

Solve the equation. Use a calculator where appropriate. If the answer is irrational, round to the nearest hundredth.
-$$\log _ { 6 } ( x - 6 ) ^ { 2 } = 2$$

Accepted Answer

A) 0, 12 
B) -6, 6 
C) 42 
D) -12, 0 
A) 0, 12 
B) -6, 6 
C) 42 
D) -12, 0

Question 8

Evaluate.
-$$4 \log _ { 9 } \sqrt [ 4 ] { 9 }$$

Accepted Answer

A) 9 
B) 36 
C) 4 
D) 1 
A) 9 
B) 36 
C) 4 
D) 1

Question 9

Solve the problem.
-If $7000 is invested at 8% compounded continuously, determine the balance in the account after 5 years.

Accepted Answer

A) $10,542.77 
B) $9800.00 
C) $10,285.30 
D) $10,442.77 
A) $10,542.77 
B) $9800.00 
C) $10,285.30 
D) $10,442.77

Question 10

Use properties of logarithms to expand the logarithmic expression as much as possible.
-$\log _ { a } \frac { x ^ { 4 } \sqrt [ 3 ] { x + 5 } } { ( x - 2 ) ^ { 2 } }$

Accepted Answer

A)  $\log _ { a } x ^ { 4 } + \log _ { a } ( x + 5 ) ^ { - 3 } - \log _ { a } ( x - 2 ) ^ { 2 }$ 
B)  $4 \log _ { a } x + \frac { 1 } { 3 } \log _ { a } ( x + 5 ) - 2 \log _ { a } ( x - 2 )$ 
C)  $\log _ { a } x ^ { 4 } + \log _ { a } ( x + 5 ) ^ { 1 / 3 } - \log _ { a } ( x - 2 ) ^ { 2 }$ 
D)  $4 \log _ { a } x - 3 \log _ { a } ( x + 5 ) - 2 \log _ { a } ( x - 2 )$ 
A)  $\log _ { a } x ^ { 4 } + \log _ { a } ( x + 5 ) ^ { - 3 } - \log _ { a } ( x - 2 ) ^ { 2 }$ 
B)  $4 \log _ { a } x + \frac { 1 } { 3 } \log _ { a } ( x + 5 ) - 2 \log _ { a } ( x - 2 )$ 
C)  $\log _ { a } x ^ { 4 } + \log _ { a } ( x + 5 ) ^ { 1 / 3 } - \log _ { a } ( x - 2 ) ^ { 2 }$ 
D)  $4 \log _ { a } x - 3 \log _ { a } ( x + 5 ) - 2 \log _ { a } ( x - 2 )$

Question 11

Write as a logarithm of a single expression.
-log11 (x + 9)+ log11 (x - 7)

Accepted Answer

A)  $\log _ { 11 } \frac { ( x + 9 ) } { ( x - 7 ) }$ 
B)  $\log _ { 11 } ( x + 9 ) ( x - 7 )$ 
C)  $\log _ { 11 } ( 2 x + 2 )$ 
D)  $\log _ { 11 } ( x + 2 )$ 
A)  $\log _ { 11 } \frac { ( x + 9 ) } { ( x - 7 ) }$ 
B)  $\log _ { 11 } ( x + 9 ) ( x - 7 )$ 
C)  $\log _ { 11 } ( 2 x + 2 )$ 
D)  $\log _ { 11 } ( x + 2 )$

Question 12

Solve the problem.
-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 bys given by $\mathrm { pH } = - \log \left( \mathrm { H } ^ { + } \right)$ wh where H+ represents the concentration of the hydrogen ions in
The solution in moles per liter. Find the pH if the hydrogen ion concentration iss $1 \times 10 ^ { - 5 }$

Accepted Answer

A) -9 
B) 9 
C) -5 
D) 5 
A) -9 
B) 9 
C) -5 
D) 5

Question 13

Use properties of logarithms to expand the logarithmic expression as much as possible.
-$\log _ { 3 } \frac { 7 } { 5 }$

Accepted Answer

A)  $\frac { \log _ { 3 } 7 } { \log _ { 3 } 5 }$ 
B)  $\log _ { 3 } 7 - \log _ { 3 } 5$ 
C)  $\log _ { 3 } 7 + \log _ { 3 } 5$ 
D)  $\log _ { 3 } 5 - \log _ { 3 } 7$ 
A)  $\frac { \log _ { 3 } 7 } { \log _ { 3 } 5 }$ 
B)  $\log _ { 3 } 7 - \log _ { 3 } 5$ 
C)  $\log _ { 3 } 7 + \log _ { 3 } 5$ 
D)  $\log _ { 3 } 5 - \log _ { 3 } 7$

Question 14

For the given functions f and g , find the indicated composition.
-$$\begin{array} { l } 
f ( x ) = \sqrt { x + 2 } , x \geq - 2 , \quad g ( x ) = 8 x - 6 \
( f \circ g ) ( x )
\end{array}$$

Accepted Answer

A)  $2 \sqrt { 2 x - 1 } , x \geq \frac { 1 } { 2 }$ 
B)  $2 \sqrt { 2 x + 1 } , x \geq - \frac { 1 } { 2 }$ 
C)  $8 \sqrt { x - 4 } , x \geq 4$ 
D)  $8 \sqrt { x + 2 } - 6 , x \geq - 2$ 
A)  $2 \sqrt { 2 x - 1 } , x \geq \frac { 1 } { 2 }$ 
B)  $2 \sqrt { 2 x + 1 } , x \geq - \frac { 1 } { 2 }$ 
C)  $8 \sqrt { x - 4 } , x \geq 4$ 
D)  $8 \sqrt { x + 2 } - 6 , x \geq - 2$

Question 15

Determine whether the function is a one-to-one function.
-$$y = x ^ { 2 } + 7 , x \geq 0$$

Accepted Answer

A) Yes 
B) No 
A) Yes 
B) No

Question 16

For the given functions f and g , find the indicated composition.
-$$\begin{array} { l } 
f ( x ) = - 2 x + 3 , \quad g ( x ) = 6 x + 9 \
( g\circ f ) ( x )
\end{array}$$

Accepted Answer

A) 12x + 27 
B) -12x - 9 
C) -12x + 21 
D) -12x + 27 
A) 12x + 27 
B) -12x - 9 
C) -12x + 21 
D) -12x + 27

Question 17

Solve the problem.
-If the magnitude of an earthquake is 2 on the Richter scale, how many times more intense is the earthquake than the smallest measurable activity?

Accepted Answer

A) 100 
B) 2 
C) 10 
D) 20 
A) 100 
B) 2 
C) 10 
D) 20

Question 18

Solve the problem.
-The function D(h)= 5(2.718)-0.4h can be used to determine the milligrams D of a certain drug in a patient's bloodstream h hours after the drug has been given. How many milligrams,rounded to two decimal places, will
Be present after 8 hours?

Accepted Answer

A) 1.08 mg 
B) 122.62 mg 
C) 0.20 mg 
D) 3.49 mg 
A) 1.08 mg 
B) 122.62 mg 
C) 0.20 mg 
D) 3.49 mg

Question 19

Solve the equation. Use a calculator where appropriate. If the answer is irrational, round to the nearest hundredth.
-$$\log _ { 3 } x = 4$$

Accepted Answer

A) 1.26 
B) 81 
C) 64 
D) 12 
A) 1.26 
B) 81 
C) 64 
D) 12

Question 20

Determine whether the given functions are inverses of each other.
-$$f ( x ) = 7 x , \quad g ( x ) = \frac { 7 } { x }$$

Accepted Answer

A) Yes 
B) No 
A) Yes 
B) No

Find the unknown value. - $\log _ { 4 } \frac { 1 } { 64 } = y$

Write the equation in logarithmic form. - $25 ^ { - 1 / 2 } = \frac { 1 } { 5 }$

Write the equation in logarithmic form. - $\mathrm { a } ^ { \mathrm { b } } = \mathrm { q }$

To what exponent must the base 10 be raised to obtain the given value? Round the answer to four decimal places. -0.0691

Use properties of logarithms to expand the logarithmic expression as much as possible. - $\log _ { 7 } x ^ { 2 } ( x - 7 )$

Use properties of logarithms to expand the logarithmic expression as much as possible. - $\log _ { 8 } x ^ { 3 }$

Solve the equation. Use a calculator where appropriate. If the answer is irrational, round to the nearest hundredth. - $\log _ { 6 } ( x - 6 ) ^ { 2 } = 2$

Evaluate. - $4 \log _ { 9 } \sqrt [ 4 ] { 9 }$

Solve the problem. -If $7000 is invested at 8% compounded continuously, determine the balance in the account after 5 years.

Use properties of logarithms to expand the logarithmic expression as much as possible. - $\log _ { a } \frac { x ^ { 4 } \sqrt [ 3 ] { x + 5 } } { ( x - 2 ) ^ { 2 } }$

Write as a logarithm of a single expression. -log11 (x + 9)+ log11 (x - 7)

Use properties of logarithms to expand the logarithmic expression as much as possible. - $\log _ { 3 } \frac { 7 } { 5 }$

For the given functions f and g , find the indicated composition. - f(x)=,x\geq-2,g(x)=8x-6 (f\circg)(x)

Determine whether the function is a one-to-one function. - $y = x ^ { 2 } + 7 , x \geq 0$

For the given functions f and g , find the indicated composition. - f(x)=-2x+3,g(x)=6x+9 (g\circf)(x)

Solve the problem. -If the magnitude of an earthquake is 2 on the Richter scale, how many times more intense is the earthquake than the smallest measurable activity?

Solve the problem. -The function D(h)= 5(2.718)-0.4h can be used to determine the milligrams D of a certain drug in a patient's bloodstream h hours after the drug has been given. How many milligrams,rounded to two decimal places, will Be present after 8 hours?

Solve the equation. Use a calculator where appropriate. If the answer is irrational, round to the nearest hundredth. - $\log _ { 3 } x = 4$

Determine whether the given functions are inverses of each other. - $f ( x ) = 7 x , \quad g ( x ) = \frac { 7 } { x }$

Basic Concepts

Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Polynomial Functions

Rational Expressions and Equations

Roots, Radicals, and Complex Numbers

Quadratic Functions

Characteristics of Functions and Their Graphs

Conic Sections

Sequences, Series, and Probability

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Exam 9: Exponential and Logarithmic Functions

Find the unknown value. - log⁡4164=y\log _ { 4 } \frac { 1 } { 64 } = ylog4​641​=y

Write the equation in logarithmic form. - 25−1/2=1525 ^ { - 1 / 2 } = \frac { 1 } { 5 }25−1/2=51​

Write the equation in logarithmic form. - ab=q\mathrm { a } ^ { \mathrm { b } } = \mathrm { q }ab=q