Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for Precalculus
40AYUIn Problems 39—50, find the domain of each function. f(x)=3 2log 4 ( x 2 5 )In Problems 39—50, find the domain of each function. g(x)=8+5ln(2x+3)In Problems 39—50, find the domain of each function. f(x)=ln( 1 x+1 )44AYUIn Problems 39—50, find the domain of each function. g(x) =log 5 ( x+1 x )In Problems 39—50, find the domain of each function. h( x )= log 3 ( x x1 )In Problems 39—50, find the domain of each function. f( x )= lnxIn Problems 39—50, find the domain of each function. g( x )= 1 lnxIn Problems 51-58, use a calculator to evaluate each expression. Round your answer to three decimal places. ln 5 350AYUIn Problems 51-58, use a calculator to evaluate each expression. Round your answer to three decimal places. ln 10 3 0.0452AYUIn Problems 51-58, use a calculator to evaluate each expression. Round your answer to three decimal places. ln4+ln2 log4+log254AYUIn Problems 51-58, use a calculator to evaluate each expression. Round your answer to three decimal places. 2ln5+log50 log4ln2In Problems 51-58, use a calculator to evaluate each expression. Round your answer to three decimal places. 3log80ln5 log5+ln20Find a so that the graph of f( x ) =log a x contains the point ( 2,2 ) .58AYUIn Problems 61-64, graph each function and its inverse on the same set of axes. f( x )= 3 x ; f 1 ( x )= log 3 xIn Problems 61-64, graph each function and its inverse on the same set of axes. f(x)= 4 x ; f 1 (x)= log 4 xIn Problems 61-64, graph each function and its inverse on the same set of axes. f(x)= ( 1 2 ) x ; f 1 (x)= log 1/2 xIn Problems 61-64, graph each function and its inverse on the same set of axes. f( x )= ( 1 3 ) x ; f 1 ( x )= log 1/3 xIn Problems 65-72, the graph of a logarithmic function is given. Match each graph to one of the following functions: (A) y= log 3 x (B) y= log 3 ( x ) (C) y= log 3 x (D) y= log 3 ( x ) (E) y= log 3 ( x1 ) (F) y= log 3 ( x1 ) (G) y= log 3 ( 1x ) (H) y=1 log 3 xIn Problems 65-72, the graph of a logarithmic function is given. Match each graph to one of the following functions: (A) y= log 3 x (B) y= log 3 ( x ) (C) y= log 3 x (D) y= log 3 ( x ) (E) y= log 3 ( x1 ) (F) y= log 3 ( x1 ) (G) y= log 3 ( 1x ) (H) y=1 log 3 xIn Problems 65-72, the graph of a logarithmic function is given. Match each graph to one of the following functions: (A) y= log 3 x (B) y= log 3 ( x ) (C) y= log 3 x (D) y= log 3 ( x ) (E) y= log 3 ( x1 ) (F) y= log 3 ( x1 ) (G) y= log 3 ( 1x ) (H) y=1 log 3 xIn Problems 65-72, the graph of a logarithmic function is given. Match each graph to one of the following functions: (A) y= log 3 x (B) y= log 3 ( x ) (C) y= log 3 x (D) y= log 3 ( x ) (E) y= log 3 ( x1 ) (F) y= log 3 ( x1 ) (G) y= log 3 ( 1x ) (H) y=1 log 3 xIn Problems 65-72, the graph of a logarithmic function is given. Match each graph to one of the following functions: (A) y= log 3 x (B) y= log 3 ( x ) (C) y= log 3 x (D) y= log 3 ( x ) (E) y= log 3 ( x1 ) (F) y= log 3 ( x1 ) (G) y= log 3 ( 1x ) (H) y=1 log 3 xIn Problems 65-72, the graph of a logarithmic function is given. Match each graph to one of the following functions: (A) y= log 3 x (B) y= log 3 ( x ) (C) y= log 3 x (D) y= log 3 ( x ) (E) y= log 3 ( x1 ) (F) y= log 3 ( x1 ) (G) y= log 3 ( 1x ) (H) y=1 log 3 xIn Problems 65-72, the graph of a logarithmic function is given. Match each graph to one of the following functions: (A) y= log 3 x (B) y= log 3 ( x ) (C) y= log 3 x (D) y= log 3 ( x ) (E) y= log 3 ( x1 ) (F) y= log 3 ( x1 ) (G) y= log 3 ( 1x ) (H) y=1 log 3 xIn Problems 65-72, the graph of a logarithmic function is given. Match each graph to one of the following functions: a. y= log 3 x b. y= log 3 ( x ) c. y= log 3 x d. y= log 3 ( x ) e. y= log 3 x-1 f. y= log 3 ( x1 ) g. y= log 3 ( 1x ) h. y=1 log 3 xIn Problems 73-88, use the given function f . a. Find the domain of f . b. Graph f . c. From the graph, determine the range and any asymptotes of f . d. Find f 1 , the inverse of f . e. Find the domain and the range of f 1 . f. Graph f 1 . f( x )=ln( x+4 )In Problems 73-88, use the given function f . a. Find the domain of f . b. Graph f . c. From the graph, determine the range and any asymptotes of f . d. Find f 1 , the inverse of f . e. Find the domain and the range of f 1 . f. Graph f 1 . f( x )=ln( x3 )In Problems 73-88, use the given function f . a. Find the domain of f . b. Graph f . c. From the graph, determine the range and any asymptotes of f . d. Find f 1 , the inverse of f . e. Find the domain and the range of f 1 . f. Graph f 1 . f( x )=2+lnxIn Problems 73-88, use the given function f . a. Find the domain of f . b. Graph f . c. From the graph, determine the range and any asymptotes of f . d. Find f 1 , the inverse of f . e. Find the domain and the range of f 1 . f. Graph f 1 . f( x )=ln( x )In Problems 73-88, use the given function f . a. Find the domain of f . b. Graph f . c. From the graph, determine the range and any asymptotes of f . d. Find f 1 , the inverse of f . e. Find the domain and the range of f 1 . f. Graph f 1 . f( x )=ln( 2x )3In Problems 73-88, use the given function f . a. Find the domain of f . b. Graph f . c. From the graph, determine the range and any asymptotes of f . d. Find f 1 , the inverse of f . e. Find the domain and the range of f 1 . f. Graph f 1 . f( x )=2ln( x+1 )In Problems 73-88, use the given function f . a. Find the domain of f . b. Graph f . c. From the graph, determine the range and any asymptotes of f . d. Find f 1 , the inverse of f . e. Find the domain and the range of f 1 . f. Graph f 1 . f( x )=log( x4 )+2In Problems 73-88, use the given function f . a. Find the domain of f . b. Graph f . c. From the graph, determine the range and any asymptotes of f . d. Find f 1 , the inverse of f . e. Find the domain and the range of f 1 . f. Graph f 1 . f( x )= 1 2 logx5In Problems 73-88, use the given function f . a. Find the domain of f . b. Graph f . c. From the graph, determine the range and any asymptotes of f . d. Find f 1 , the inverse of f . e. Find the domain and the range of f 1 . f. Graph f 1 . f( x )= 1 2 log( 2x )In Problems 73-88, use the given function f . a. Find the domain of f . b. Graph f . c. From the graph, determine the range and any asymptotes of f . d. Find f 1 , the inverse of f . e. Find the domain and the range of f 1 . f. Graph f 1 . f( x )=log( 2x )In Problems 73-88, use the given function f . a. Find the domain of f . b. Graph f . c. From the graph, determine the range and any asymptotes of f . d. Find f 1 , the inverse of f . e. Find the domain and the range of f 1 . f. Graph f 1 . f( x )=3+ log 3 ( x+2 )In Problems 73-88, use the given function f . a. Find the domain of f . b. Graph f . c. From the graph, determine the range and any asymptotes of f . d. Find f 1 , the inverse of f . e. Find the domain and the range of f 1 . f. Graph f 1 . f( x )=2 log 3 ( x+1 )In Problems 73-88, use the given function f . a. Find the domain of f . b. Graph f . c. From the graph, determine the range and any asymptotes of f . d. Find f 1 , the inverse of f . e. Find the domain and the range of f 1 . f. Graph f 1 . f(x)= e x+2 3In Problems 73-88, use the given function f . a. Find the domain of f . b. Graph f . c. From the graph, determine the range and any asymptotes of f . d. Find f 1 , the inverse of f . e. Find the domain and the range of f 1 . f. Graph f 1 . f(x)=3 e x +2In Problems 73-88, use the given function f . a. Find the domain of f . b. Graph f . c. From the graph, determine the range and any asymptotes of f . d. Find f 1 , the inverse of f . e. Find the domain and the range of f 1 . f. Graph f 1 . f(x) =2 x/3 +486AYUIn Problems 89-112, solve each equation. log 3 x=2In Problems 89-112, solve each equation. log 5 x=3In Problems 89112, solve each equation. log2(3x+4)=5In Problems 89-112, solve each equation. log 3 (3x2)=2In Problems 89112, solve each equation. logx16=2In Problems 89-112, solve each equation. log x ( 1 8 )=3In Problems 89-112, solve each equation. ln e x =5In Problems 89-112, solve each equation. ln e 2x =8In Problems 89-112, solve each equation. log 4 64=xIn Problems 89-112, solve each equation. log 5 625=xIn Problems 89-112, solve each equation. log 3 243=2x+198AYUIn Problems 89-112, solve each equation. e 3x =10In Problems 89-112, solve each equation. e 2x = 1 3In Problems 89-112, solve each equation. e 2x+5 =8102AYUIn Problems 89-112, solve each equation. log 3 ( x 2 +1 )=2104AYUIn Problems 89-112, solve each equation. log 2 8 x =3106AYUIn Problems 89-112, solve each equation. 5 e 0.2x =7In Problems 89-112, solve each equation. 8 10 2x7 =3In Problems 89-112, solve each equation. 2 10 2x =5In Problems 89-112, solve each equation. 4 e x+1 =5Suppose that G( x )= log 3 ( 2x+1 )2 . a. What is the domain of G ? b. What is G( 40 ) ? What point is on the graph of G ? c. If G(x)=3 , what is x ? What point is on the graph of G ? d. What is the zero of G ?Suppose that F(x)= log 2 ( x+1 )3 . a. What is the domain of F ? b. What is F( 7 ) ? What point is on the graph of F ? c. If F(x)=1 , what is x ? What point is on the graph of F ? d. What is the zero of F ?113AYU114AYU115AYU116AYUChemistry The pH of a chemical solution is given by the formula pH=log10[H+] Where [H+] is the concentration of hydrogen ions in moles per liter. Values of pH range from 0 (acidic) to 14 (alkaline). What is the pH of a solution for which [H+] is 0.1? What is the pH of a solution for which [H+] is 0.01? What is the pH of a solution for which is [H+] is 0.001? What happens to pH as the hydrogen ion concentration decreases? Determine the hydrogen ion concentration of an orange (pH=3.5), Determine the hydrogen ion concentration of human blood (pH=7.4).118AYUAtmospheric Pressure The atmospheric pressure p on an object decreases with increasing height. This pressure, measured in millimeters of mercury, is related to the height h(in kilometers) above sea level by the Junction p(h)=760e0.145h Find the height of an aircraft if the atmospheric pressure is 320 millimeters of mercury. Find the height of a mountain if the atmospheric pressure is 667 millimeters of mercury.Healing of Wounds The normal healing of wounds can he modeled by an exponential function. If A0 represents the original area of the wound, and if A equals the area of the wound, then the function A(n)=A0e0.35n describes the area of a wound alter n days following an injury when no infection is present to retard the healing. Suppose that a wound initially had an area of 100 square millimeter, If healing is taking place, after how many days will the wound he one-half its original size? How long before the wound is 10 of its original size?121AYU122AYUDrug Medication The function D(h)=5e0.4h can be used to find the number of milligrams D of a certain drug that is in a patient's bloodstream h hours after the drug was administered, When the number of milligrams reaches 2, the drug is to beadministered again. What is the time between injections?Spreading of Rumors A model for the number N of people in a college community who have heard a certain rumor is N(d)=P(1e0.15d) where P is the total population of the community and d is the number of days that have elapsed since the rumor began. In a community of 1000 students, how many days will elapse before 450 students have heard the rumor?125AYU Learning Curve Psychologists sometimes use the function
to measure the amount learned at time. Here represents the amount to he learned, and the number measures the rate of learning. Suppose that a student has an amount of vocabulary words to learn. A psychologist determines that the student has learned vocabulary words after minutes.
Determine the rate of learning.
Approximately how many words will the student have learned after minutes?
After minutes?
How long does it take for the student to learn words?
127AYU128AYU129AYU130AYU131AYU132AYU Alcohol and Driving The concentration of alcohol in a person’s bloodstream is measurable. Suppose that the relative risk of having an accident while driving a car can be modelled by an equation of the form
where is the percent concentration of alcohol in the bloodstream and is a constant.
Suppose that a concentration of alcohol in the bloodstream of percent results in a relative risk of an accident of Find the constant in the equation.
Using this value of what is the relative risk if the concentration is percent
Using the same value of what concentration of alcohol corresponds to a relative risk of
If the law asserts that anyone with a relative risk of having an accident of or more should not have driving privileges, at what concentration of alcohol in the bloodstream should a driver be arrested and charged with a
Compare this situation with that of Example If you were a lawmaker, which situation would you supportGive your reasons.
134AYU135AYU136AYU1AYU2AYU3AYU4AYU5AYU6AYU7AYU8AYU9AYU10AYU11AYU12AYU13AYU14AYU15AYU16AYU17AYU18AYU19AYU20AYU21AYU22AYU23AYU24AYU25AYU26AYU27AYU28AYU29AYU30AYU31AYU32AYU33AYU34AYU35AYU36AYU37AYU38AYU39AYU40AYU41AYU42AYU43AYU44AYU45AYU46AYU47AYU48AYU49AYU50AYU51AYU52AYU53AYU54AYU55AYU56AYU57AYU58AYU59AYU60AYU61AYU62AYU63AYU64AYU65AYU66AYU67AYU68AYU69AYU70AYU71AYU72AYU73AYU74AYU75AYU76AYU77AYU78AYU79AYU80AYU81AYU82AYU83AYU84AYU85AYU86AYU87AYU88AYU89AYU90AYU91AYU92AYU93AYU94AYU95AYU96AYU97AYU98AYU99AYU100AYU101AYU102AYU103AYU104AYU105AYU106AYU107AYU108AYU109AYU110AYU111AYU112AYU113AYU114AYUSolve x 2 7x30=0 . (pp.A47-A52)2AYU3AYUApproximate the solution(s) to x 3 2x+2=0 using a graphing utility. (pp. 26-28)5AYU6AYU7AYU8AYU9AYU10AYU11AYU12AYU13AYU14AYU15AYU16AYU17AYU18AYU19AYU20AYU21AYU22AYU23AYU24AYU25AYU26AYU27AYU28AYU29AYU30AYU31AYU32AYUIn Problems 41-68, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 2 x5 =8In Problems 41-68, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 5 x =25In Problems 41-68, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 2 x =10In Problems 41-68, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 3 x =14In Problems 41-68, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 8 x =1.2In Problems 41-68, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 5( 2 3x )=8In Problems 41-68, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 5 x =25In Problems 41-68, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 0.3( 4 0.2x )=0.2In Problems 41-68, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 3 12x = 4 xIn Problems 41-68, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 2 x+1 = 5 12xIn Problems 41-68, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. ( 3 5 ) x = 7 1xIn Problems 41-68, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. ( 4 3 ) 1-x = 5 xIn Problems 41-68, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 1.2 x = ( 0.5 ) xIn Problems 41-68, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 0.3 1+x = 1.7 2x1In Problems 41-68, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 1-x = e xIn Problems 41-68, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. e x+3 = xIn Problems 41-68, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 2 2x + 2 x 12=0In Problems 41-68, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 3 2x + 3 x 2=0In Problems 41-68, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 3 2x + 3 x+1 4=0In Problems 41-68, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 2 2x + 2 x+2 12=0In Problems 41-68, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 16 x + 4 x+1 3=0In Problems 41-68, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 9 x 3 x1 +1=0In Problems 41-68, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 25 x 8.5 x =16In Problems 41-68, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 36 x 6.6 x =9In Problems 41-68, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 3.4 x + 4.2 x +8=0In Problems 41-68, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 2.49 x + 11.7 x +5=0In Problems 41-68, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 4 x 10.4 x =3In Problems 41-68, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 3 x 14.3 x =5In Problems 69-82, use a graphing utility to solve each equation. Express your answer rounded to two decimal places. log 5 ( x+1 ) log 4 ( x2 )=1In Problems 69-82, use a graphing utility to solve each equation. Express your answer rounded to two decimal places. log 2 ( x1 ) log 6 ( x+2 )=2In Problems 69-82, use a graphing utility to solve each equation. Express your answer rounded to two decimal places. e x =xIn Problems 69-82, use a graphing utility to solve each equation. Express your answer rounded to two decimal places. e 2x =x+2In Problems 69-82, use a graphing utility to solve each equation. Express your answer rounded to two decimal places. e x = x 2In Problems 69-82, use a graphing utility to solve each equation. Express your answer rounded to two decimal places. e x = x 3In Problems 69-82, use a graphing utility to solve each equation. Express your answer rounded to two decimal places. lnx=xIn Problems 69-82, use a graphing utility to solve each equation. Express your answer rounded to two decimal places. ln( 2x )=x+2In Problems 69-82, use a graphing utility to solve each equation. Express your answer rounded to two decimal places. lnx= x 3 1In Problems 69-82, use a graphing utility to solve each equation. Express your answer rounded to two decimal places. lnx= x 2In Problems 69-82, use a graphing utility to solve each equation. Express your answer rounded to two decimal places. e x +lnx=4In Problems 69-82, use a graphing utility to solve each equation. Express your answer rounded to two decimal places. e x lnx=473AYUIn Problems 69-82, use a graphing utility to solve each equation. Express your answer rounded to two decimal places. e x =lnx75AYU76AYU77AYU78AYU79AYU80AYU81AYU82AYU83AYU84AYU85AYU86AYU87AYU88AYU89AYU