Question 1

Change the logarithmic expression to an equivalent expression involving an exponent.
-$\log _ { 5 } 25 = x$

Accepted Answer

A)  $5 ^ { \mathrm { x } } = 25$ 
B)  $25 ^ { x } = 5$ 
C)  $x ^ { 5 } = 25$ 
D)  $25 ^ { 5 } = x$ 
A)  $5 ^ { \mathrm { x } } = 25$ 
B)  $25 ^ { x } = 5$ 
C)  $x ^ { 5 } = 25$ 
D)  $25 ^ { 5 } = x$

Question 2

Write as the sum and/or difference of logarithms. Express powers as factors.
-$\log _ { 2 } \left( \frac { x + 5 } { x ^ { 7 } } \right)$

Accepted Answer

A)  $\log _ { 2 } ( x + 5 ) - 7 \log _ { 2 } x$ 
B)  $\log _ { 2 } ( x + 5 ) + 7 \log _ { 2 } x$ 
C)  $\log _ { 2 } ( x + 5 ) - \log _ { 2 } x$ 
D)  $7 \log _ { 2 } x - \log _ { 2 } ( x + 5 )$ 
A)  $\log _ { 2 } ( x + 5 ) - 7 \log _ { 2 } x$ 
B)  $\log _ { 2 } ( x + 5 ) + 7 \log _ { 2 } x$ 
C)  $\log _ { 2 } ( x + 5 ) - \log _ { 2 } x$ 
D)  $7 \log _ { 2 } x - \log _ { 2 } ( x + 5 )$

Question 3

Indicate whether the function is one-to-one.
-{(3, -12), (7, 4), (12, -8)}

Accepted Answer

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

Question 4

Solve the problem.
-Carla has just inherited a building that is worth $250,000. The building is in a high demand area, and the value
of the building is projected to increase at a rate of 25% per year for the next 4 years. How much more money
will she make if she waits four years to sell the building instead of selling now?

Accepted Answer

The answer of Solve the problem.
-Carla has just inherited a...

Question 5

Find functions f and g so that f $f \circ g = H$
-$$H ( x ) = \frac { 6 } { \sqrt { 9 x + 10 } }$$

Accepted Answer

A)  $f ( x ) = 6 ; \quad g ( x ) = \sqrt { 9 + 10 }$ 
B)  $f ( x ) = \frac { 6 } { x } ; \quad g ( x ) = 9 x + 10$ 
C)  $f ( x ) = \frac { 6 } { \sqrt { x } } ; \quad g ( x ) = 9 x + 10$ 
D)  $f ( x ) = \sqrt { 9 x + 10 } ; g ( x ) = 6$ 
A)  $f ( x ) = 6 ; \quad g ( x ) = \sqrt { 9 + 10 }$ 
B)  $f ( x ) = \frac { 6 } { x } ; \quad g ( x ) = 9 x + 10$ 
C)  $f ( x ) = \frac { 6 } { \sqrt { x } } ; \quad g ( x ) = 9 x + 10$ 
D)  $f ( x ) = \sqrt { 9 x + 10 } ; g ( x ) = 6$

Question 6

Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to two decimal places.
-$\log _ { 3,9 } 10$

Accepted Answer

A)  1.69 
B)  1.00 
C)  2.56 
D)  0.59 
A)  1.69 
B)  1.00 
C)  2.56 
D)  0.59

Question 7

Solve the equation.
-$$8 ^ { x - 3 } = 64 ^ { 4 x }$$

Accepted Answer

A)  $\left\{ - \frac { 3 } { 7 } \right\}$ 
B)  $\left\{ - \frac { 1 } { 7 } \right\}$ 
C)  $\{ - 1 \}$ 
D)  $\left\{ - \frac { 9 } { 7 } \right\}$ 
A)  $\left\{ - \frac { 3 } { 7 } \right\}$ 
B)  $\left\{ - \frac { 1 } { 7 } \right\}$ 
C)  $\{ - 1 \}$ 
D)  $\left\{ - \frac { 9 } { 7 } \right\}$

Question 8

Solve the problem.
-A cancer patient undergoing chemotherapy is injected with a particular drug. The function $\mathrm { D } ( \mathrm { h } ) = 4 \mathrm { e } ^ { - 0.35 \mathrm {~h} }$ gives the number of milligrams D of this drug that is in the patient's bloodstream h hours after the drug has
been administered. How many milligrams of the drug were injected? To the nearest milligram, how much of the
drug will be present after 2 hours?

Accepted Answer

The answer of Solve the problem.
-A cancer patient undergoing chemotherapy...

Question 9

Find the domain of the composite function f $f ^ { \circ } g $
-$$f ( x ) = \frac { 1 } { x - 7 } ; \quad g ( x ) = \sqrt { x - 1 }$$

Accepted Answer

A)  $\{ x \mid x \geq 1 , x \neq 7 \}$ 
B)  $\{ x \mid x \geq 1 , x \neq 7 , x \neq 50 \}$ 
C)  $\{ x \mid x$ is any real number $\}$ 
D)  $\{ x \mid x \geq 1 , x \neq 50 \}$ 
A)  $\{ x \mid x \geq 1 , x \neq 7 \}$ 
B)  $\{ x \mid x \geq 1 , x \neq 7 , x \neq 50 \}$ 
C)  $\{ x \mid x$ is any real number $\}$ 
D)  $\{ x \mid x \geq 1 , x \neq 50 \}$

Question 10

Find functions f and g so that f $f \circ g = H$
-$$H ( x ) = \left( 5 - 2 x ^ { 3 } \right) ^ { 2 }$$

Accepted Answer

A)  $f ( x ) = 5 - 2 x ^ { 3 } ; g ( x ) = x ^ { 2 }$ 
B)  $f ( x ) = x ^ { 2 } ; g ( x ) = 5 - 2 x ^ { 3 }$ 
C)  $f ( x ) = ( 5 - 2 x ) ^ { 3 } ; g ( x ) = x ^ { 2 }$ 
D)  $f ( x ) = x ^ { 3 } ; g ( x ) = ( 5 - 2 x ) ^ { 2 }$ 
A)  $f ( x ) = 5 - 2 x ^ { 3 } ; g ( x ) = x ^ { 2 }$ 
B)  $f ( x ) = x ^ { 2 } ; g ( x ) = 5 - 2 x ^ { 3 }$ 
C)  $f ( x ) = ( 5 - 2 x ) ^ { 3 } ; g ( x ) = x ^ { 2 }$ 
D)  $f ( x ) = x ^ { 3 } ; g ( x ) = ( 5 - 2 x ) ^ { 2 }$

Question 11

Write as the sum and/or difference of logarithms. Express powers as factors.
-$\log _ { 7 } \frac { \sqrt [ 2 ] { 15 } } { y ^ { 2 } x }$

Accepted Answer

A)  $\frac { 1 } { 2 } \log _ { 7 } 15 - 2 \log _ { 7 } y - 2 \log _ { 7 } x$ 
B)  $\frac { 1 } { 2 } \log _ { 7 } 15 - 2 \log _ { 7 } y - \log _ { 7 } x$ 
C)  $\log _ { 19 } 5 - \log _ { 19 } n - \log _ { 19 } \mathrm {~m}$ 
D)  $2 \log _ { 7 } 15 - 2 \log _ { 7 } y - \log _ { 7 } 2$ 
A)  $\frac { 1 } { 2 } \log _ { 7 } 15 - 2 \log _ { 7 } y - 2 \log _ { 7 } x$ 
B)  $\frac { 1 } { 2 } \log _ { 7 } 15 - 2 \log _ { 7 } y - \log _ { 7 } x$ 
C)  $\log _ { 19 } 5 - \log _ { 19 } n - \log _ { 19 } \mathrm {~m}$ 
D)  $2 \log _ { 7 } 15 - 2 \log _ { 7 } y - \log _ { 7 } 2$

Question 12

Decide whether or not the functions are inverses of each other.
-$$f ( x ) = 5 x ^ { 2 } + 1 , g ( x ) = \sqrt { \frac { x - 1 } { 5 } }$$

Accepted Answer

A)  Yes; Exclude the interval $( - \infty , 1 )$ 
B)  No 
C)  Yes; No values need to be excluded. 
D)  Yes; Exclude the interval $( - \infty , 5 )$ 
A)  Yes; Exclude the interval $( - \infty , 1 )$ 
B)  No 
C)  Yes; No values need to be excluded. 
D)  Yes; Exclude the interval $( - \infty , 5 )$

Question 13

Find the inverse of the function and state its domain and range .
-$\{ ( - 5 , - 3 ) , ( 3,5 ) , ( 1,1 ) , ( - 1 , - 1 ) \}$

Accepted Answer

A)  $\{ ( - 3 , - 5 ) , ( 5,3 ) , ( 1,1 ) , ( - 1 , - 1 ) \} \mathrm { D } = \{ - 3,5,1 , - 1 \} ; \mathrm { R } = \{ - 5,3,1 , - 1 \}$ 
B)  $\left\{ \left( - 5 , - \frac { 1 } { 3 } \right) , \left( 3 , \frac { 1 } { 5 } \right) , ( 1,1 ) , ( - 1 , - 1 ) \right\} \mathrm { D } = \{ - 5,3,1 , - 1 \} , \mathrm { R } = \left\{ - \frac { 1 } { 3 } , \frac { 1 } { 5 } , 1 , - 1 \right\}$ 
C)  $\{ ( - 1,1 ) , ( 5,3 ) , ( - 3,3 ) , ( 1 , - 1 ) \} ; \mathrm { D } = \{ ( - 1,5 , - 3,1 \} ; \mathrm { R } = \{ 1,3 , - 1 \}$ 
D)  $\{ ( - 1,1 ) , ( 1,3 ) , ( - 3 , - 5 ) , ( 1 , - 1 ) \} ; \mathrm { D } = \{ - 1,1 , - 3,1 \} ; \mathrm { R } = \{ 1,3 , - 5 , - 1 \}$ 
A)  $\{ ( - 3 , - 5 ) , ( 5,3 ) , ( 1,1 ) , ( - 1 , - 1 ) \} \mathrm { D } = \{ - 3,5,1 , - 1 \} ; \mathrm { R } = \{ - 5,3,1 , - 1 \}$ 
B)  $\left\{ \left( - 5 , - \frac { 1 } { 3 } \right) , \left( 3 , \frac { 1 } { 5 } \right) , ( 1,1 ) , ( - 1 , - 1 ) \right\} \mathrm { D } = \{ - 5,3,1 , - 1 \} , \mathrm { R } = \left\{ - \frac { 1 } { 3 } , \frac { 1 } { 5 } , 1 , - 1 \right\}$ 
C)  $\{ ( - 1,1 ) , ( 5,3 ) , ( - 3,3 ) , ( 1 , - 1 ) \} ; \mathrm { D } = \{ ( - 1,5 , - 3,1 \} ; \mathrm { R } = \{ 1,3 , - 1 \}$ 
D)  $\{ ( - 1,1 ) , ( 1,3 ) , ( - 3 , - 5 ) , ( 1 , - 1 ) \} ; \mathrm { D } = \{ - 1,1 , - 3,1 \} ; \mathrm { R } = \{ 1,3 , - 5 , - 1 \}$

Question 14

Solve the equation.
-$$3 ^ { x } = \frac { 1 } { 27 }$$

Accepted Answer

A)  $\left\{ \frac { 1 } { 9 } \right\}$ 
B)  $\left\{ \frac { 1 } { 3 } \right\}$ 
C)  $\{ 3 \}$ 
D)  $\{ - 3 \}$ 
A)  $\left\{ \frac { 1 } { 9 } \right\}$ 
B)  $\left\{ \frac { 1 } { 3 } \right\}$ 
C)  $\{ 3 \}$ 
D)  $\{ - 3 \}$

Question 15

The loudness of a sound of intensity x, measured in watts per square meter, is defined as L( $$L ( x ) = \log \left( \frac { x } { x _ { 0 } } \right) , \text { where } x _ { 0 } = 10 ^ { - 3 }$$
-A company with load machinery needs to cut its sound intensity to 72% of its original level. By how many
decibels should the loudness be reduced?

Accepted Answer

The answer of The loudness of a sound of intensity...

Question 16

Solve the problem.
-Suppose that $f ( x ) = 5 ^ { x } + 9$. What is $f ( 5 )$ ? What point is on the graph of $f$ ?

Accepted Answer

A)  3,$125 ; ( 9,3,125 )$ 
B)  3,$134 ; ( 5,3,125 )$ 
C)  3,$125 ; ( 5,3,125 )$ 
D)  3,$134 ; ( 5,3,134 )$ 
A)  3,$125 ; ( 9,3,125 )$ 
B)  3,$134 ; ( 5,3,125 )$ 
C)  3,$125 ; ( 5,3,125 )$ 
D)  3,$134 ; ( 5,3,134 )$

Question 17

Use the properties of logarithms to find the exact value of the expression. Do not use a calculator.
-$4 ^ { \log _ { 4 } 0.473 }$

Accepted Answer

A)  477 
B)  4 
C)  $2.114$ 
D)  $0.473$ 
A)  477 
B)  4 
C)  $2.114$ 
D)  $0.473$

Question 18

Solve the problem.
-The volume $\mathrm { V }$ (in cubic inches) of a cylindrical pipe with length 12 inches is given by $\mathrm { V } ( \mathrm { r } ) = 12 \pi \mathrm { r } ^ { 2 }$, where $r$ is the radius of the piston (in inches). If the radius is increasing with time $t$ (in minutes) according to the formula $r ( t ) = \frac { 1 } { 6 } t ^ { 2 } , t \geq 0$, find the volume $V$ of the pipe as a function of the time $t$

Accepted Answer

The answer of Solve the problem.
-The volume \(\mathrm { V...

Question 19

Solve the problem.
-Assume that the half-life of Carbon-14 is 5700 years. Find the age (to the nearest year) of a wooden axe in
which the amount of Carbon-14 is 30% of what it originally had.

Accepted Answer

The answer of Solve the problem.
-Assume that the half-life of...

Question 20

Find functions f and g so that f $f \circ g = H$
-$$\mathrm { H } ( \mathrm { x } ) = \sqrt { \frac { 1 } { \mathrm { x } - 2 } }$$

Accepted Answer

A)  $g ( x ) = \sqrt { x } ; f ( x ) = \frac { 1 } { x - 2 }$ 
B)  $f ( x ) = x - 2 ; g ( x ) = \frac { 1 } { \sqrt { x } }$ 
C)  $f ( x ) = \frac { 1 } { x - 2 } ; g ( x ) = \sqrt { x }$ 
D)  $f ( x ) = \frac { 1 } { x - 2 } ; g ( x ) = \frac { 1 } { \sqrt { x } }$ 
A)  $g ( x ) = \sqrt { x } ; f ( x ) = \frac { 1 } { x - 2 }$ 
B)  $f ( x ) = x - 2 ; g ( x ) = \frac { 1 } { \sqrt { x } }$ 
C)  $f ( x ) = \frac { 1 } { x - 2 } ; g ( x ) = \sqrt { x }$ 
D)  $f ( x ) = \frac { 1 } { x - 2 } ; g ( x ) = \frac { 1 } { \sqrt { x } }$

Change the logarithmic expression to an equivalent expression involving an exponent. - $\log _ { 5 } 25 = x$

Write as the sum and/or difference of logarithms. Express powers as factors. - $\log _ { 2 } \left( \frac { x + 5 } { x ^ { 7 } } \right)$

Indicate whether the function is one-to-one. -{(3, -12), (7, 4), (12, -8)}

Find functions f and g so that f $f \circ g = H$ - $H ( x ) = \frac { 6 } { \sqrt { 9 x + 10 } }$

Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to two decimal places. - $\log _ { 3,9 } 10$

Solve the equation. - $8 ^ { x - 3 } = 64 ^ { 4 x }$

Find the domain of the composite function f $f ^ { \circ } g$ - $f ( x ) = \frac { 1 } { x - 7 } ; \quad g ( x ) = \sqrt { x - 1 }$

Find functions f and g so that f $f \circ g = H$ - $H ( x ) = \left( 5 - 2 x ^ { 3 } \right) ^ { 2 }$

Write as the sum and/or difference of logarithms. Express powers as factors. - $\log _ { 7 } \frac { \sqrt [ 2 ] { 15 } } { y ^ { 2 } x }$

Decide whether or not the functions are inverses of each other. - $f ( x ) = 5 x ^ { 2 } + 1 , g ( x ) = \sqrt { \frac { x - 1 } { 5 } }$

Find the inverse of the function and state its domain and range . - $\{ ( - 5 , - 3 ) , ( 3,5 ) , ( 1,1 ) , ( - 1 , - 1 ) \}$

Solve the equation. - $3 ^ { x } = \frac { 1 } { 27 }$

Solve the problem. -Suppose that $f ( x ) = 5 ^ { x } + 9$ . What is $f ( 5 )$ ? What point is on the graph of $f$ ?

Use the properties of logarithms to find the exact value of the expression. Do not use a calculator. - $4 ^ { \log _ { 4 } 0.473 }$

Solve the problem. -Assume that the half-life of Carbon-14 is 5700 years. Find the age (to the nearest year) of a wooden axe in which the amount of Carbon-14 is 30% of what it originally had.

Find functions f and g so that f $f \circ g = H$ - $\mathrm { H } ( \mathrm { x } ) = \sqrt { \frac { 1 } { \mathrm { x } - 2 } }$

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Review

Filters

Exam 4: Exponential and Logarithmic Functions

Change the logarithmic expression to an equivalent expression involving an exponent. - log⁡525=x\log _ { 5 } 25 = xlog5​25=x

Write as the sum and/or difference of logarithms. Express powers as factors. - log⁡2(x+5x7)\log _ { 2 } \left( \frac { x + 5 } { x ^ { 7 } } \right)log2​(x7x+5​)