Logarithms Questions and Answers

Use the logarithm change of base formula to convert each of the following logarithms to the specified base Then use a calculator to approximate the logarithm Round approximations to four decimal places Convert log 1 2 from base 11 to base 2 log 12 log 11 log 12 Convert log 12 from base 9 to base e x which is approximately equal to 0 2891 log 12 log 1 x which is approximately equal to 1 1309 of

Let N t be the number of people at a school who have heard a certain rumor Suppose that this can be modeled by the function 140 N t 2 8e 0 5t where t is time in days Part 1 How many people have heard the rumor after 3 days Round your answer to the nearest whole number people Part 2 What number of people will have heard the rumor in the long run Round your answer to the nearest whole number A graph is one way to approach this question people

A doctor prescribes 250 mg of a drug The amount of the drug in the patient s body decays by 40 every Part 1 Write an exponential model for the A t the amount of the drug in the patient s system after t hours have passed A t help formulas Part 2 Use your formula to find the amount of the drug remaining after 3 hours have passed Round your answer to the nearest tenth help numbers mg hour Part 3 What is the half life of this drug Round your answer to the nearest whole number hours

e g The area between the curve y 17 7 2 71 Determine whether the following statements are true and give an explanation or counterexample Assume x 0 and y 0 a In xy Inx Iny b In 0 1 c In x y Inx Iny d Part 3 of 7 f 32 for any integer n21 and the x axis on the interval 1 e is 1 OA The statement is false because In 0 0 OB The statement is true because 1 C The statement is false The natural logarithmic function In x is not defined at x 0 D The statement is true because in 0 1 c Choose the correct answer below HW Score 69 05 16 57 of Points 0 14 of 1 OA The statement is false The Product Rule of Logarithms states that in x In y In xy OB The statement is false The Difference Rule of Logarithms states that inx Iny In x y OC The statement is true The Difference Rule of Logarithms states that In x y Inx Iny OD The statement is true The Sum Rule of Logarithms states that in x y Inx Iny

the ratio of carbon 14 to carbon 12 in a piece of wood discovered in a cave is R 1 915 Estimate the age of the piece of wood Round your answer to the nearest whole num x years old

5 Find the exact value of each trigonometric expression a cos 70 cos 50 sin 70 sin 50 5 Cos 70 50 os 120 21 1 5 b cos 1 12 Cos os 2 233 1 12x 17 55 1 1 2 3 2 2 5 6 Find the exact value of tan 285 10

sin 0 Question Help Video 7 If cos 0 and is in the 4th quadrant find the exact value for sin 0 8

Question 5 A wooden artifact from an ancient tomb contains 20 percent of the carbon 14 that is present in living trees How long ago to the nearest year was the artifact made The half life of carbon 14 is 5730 years years ele Video G

Listed below are the top 10 annual salaries in millions of dollars of TV personalities Find the a mean b median and c mode for the given sample data in millions of dollars 38 2 35 4 34 6 27 8 15 4 13 12 8 10 2 9 2 8 1 a The mean is Type an integer or a decimal b The median is Type an integer or a decimal c Select the correct choice below and fill in any answer boxes in your choice A The mode is Use a comma to separate answers as needed OB There is no mode

0710 pts 4x 17 thon Details

0 10 pts 3299 Details Use the like bases property and exponents to solve the equation 10 n 2 108n 3

x 4y20 28 Write expression log logarithms with no exponents Simplify your answer completely 1420 as a sum or difference of

0 10 pts 3299 Details Write the following as the sum and or difference of logarithms Assume all variables are positive log 8c 6 The answer format in lowercase characters is log number Spaces in the answer are optional

0 10 pts 399 Details Evaluate the following expressions Your answers must be exact and in simplest form a ln e b eln2 3 c en 4 1

0 10 pts 3299 Details Evaluate using your calculator giving at least 3 decimal places Jog 810

0 10 pts 399 Details Find the logarithm log 1 100 000

0 10 pts 399 Details Find the logarithm 1 log4 256

0 10 pts 399 Details

Determine the parent function from which the graph of the function shown below can be otained Next identify each transformation that can be applied to the parent function in order to obtain the graph of the function shown below 5 g x a Choose the correct parent function 6 y 1 Oy 5 6 Oy logg x Oy logs x b Choose the correct transformation Reflections Select an answer c Choose the correct transformation Stretches Compressions Select an answer d Choose the correct transformation Vertical Shifts Select an answer e Choose the correct transformation Horizontal Shifts Select an answer

A heat engine has a heat input of 3 x 104 Btu h and a thermal efficiency of 40 0 percent Calculate the power it will produce in hp Source 3 x 104 Btu h HE Sink th The power produced is hp

Given the Initial Value and Rate of Change write the exponential function for each of the following Initial Value 131 626 2166 2233 2996 4924 Rate Growth Rate 16 Growth Rate 6 Growth Rate 7 5 Growth Rate 116 Decay Rate 26 Decay Rate 3 f x f x f x f x f x f x Function

Solve the problem If 9 1 what does 81 equal 000 4 16 16 1 0 16

formula D 50e 0 5h 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 4 the drug is to be administered again What is the time between injections The time between injections is

Change the exponential statement to an equivalent statement involving a logarithm 1 9 a 02 log1 9 01 9 log2 01 9 log2a a log 1 9

Solve the equation log2169 2 The solution is I Type integers or simplified fractions

Use the properties of logarithms to evaluate each of the following expressions a 2log 3 log 36 b Inelne 0

1 nd I ad 1 2 2 dz dz C Iz 5 4 CCW

The speedometer of a car is designed to be accurate with tires that are 35 6 cm in radius If the tires are changed to 38 1 cm in radius and the speedometer shows 88 km hr how fast is the car actually going A 94 2 km hr B 75 8 km hr 99 8 km hr 82 9 km hr

Use properties of logarithms to completely expand the logarithmic expression Wherever possible evaluate logarithmic expressions 8 R T

Determine the inverse of y f x 2 ln x 6 A f y 2 e 6 B f y e 6 C f y 2 e 6 D f y e 6 E f y 6 ln y 2

K In the set of the ten top grossing movies of all time shown in the table available below define the sets as shown below M the set of movies that earned more than 1 5 billion L the set of movies that earned less than 2 billion B the set of movies that were made before 2015 Describe the set L M U B in words and then find the set Click on the icon to view the table of the ten top grossing movies of all time CITE Describe the set L M U B in words Choose the correct answer below A The set of movies that earned less than 2 billion that did not earn less than 1 5 billion or were made before 2015 B The set of movies that earned more than 2 billion or earned less than 1 5 billion or were made before 2015 C The set of movies that earned less than 2 billion that did not earn more than 1 5 billion or were not made before 2015 OD The set of movies that earned less than 2 billion that did not earn more than 1 5 billion or were made before 2015 Identify the elements of the set L M U B Type the letter s of the movie s that is are in the specified set For example an answer could be B a b d g h j L M U B Use a comma to separate answers as needed Table of the Ten Top Grossing Movies Movie Movie a Movie b Movie c Movie d Movie e Movie f Movie g Year 1996 1994 2015 1992 2015 2015 2010 Gross billions 2 9 2 3 1 8 1 5 1 5 1 4 1 3

This question 1 point s possible Consider the following sets U upperclassmen L lowerclassmen S science majors V GPA above 3 0 A art majors T Athletes and D involved in Drama Use the table of students shown to the right to answer the following question Find the number of subsets of the set of students who are upperclassmen and have a GPA above 2 7 Type a whole number Major Allen English Belinda Physics Carmen English Dana History Elston Sociology Frank Art Gina Art Hector Art Ivana History James History 3 8 Basketball 3 8 Newspaper 1 8 Drama Class Rank GPA Activities Freshman 2 2 Band Senior Sophomore Freshman Senior Sophomore 3 1 Baseball Junior 3 8 Drama Freshman 2 1 Band Senior 3 4 Football Freshman 2 7 Newspaper 2 9 Newspaper

y log 3 X Choose the correct graph below OA OB Q O C Ay

Express the following as a sum difference or multiple of logarithms log 5 3 a log 5 3

Exponential Logarithmic Functions Cour If the population of squirrels on campus t years after the beginning of 1855 is given by the logistic growth function 3000 1 8e 1 21t find the time t such that s t 2400 Time t s t which when rounded to two decimal places corresponds to the year

10 4 points Braydon can afford to pay approximately 1400 per month on his mortgage Determine the difference between the amounts paid in one year using bi weekly payments and accelerated bi weekly payments

men a person in California renews the registration for an automobile the bar graph shown below is included with the bill BAC Zones 90 to 109 lbs TOTAL DRINKS 110 to 129 lbs TOTAL DRINKS 130 to 149 lbs TOTAL DRINKS TIME FROM 1st DRINK 2345678123456781234567812345678 1 hr 2 hrs 3 hrs 4 hrs 190 to 209 lbs TOTAL DRINKS BAC Zones 170 to 189 lbs 210 to 229 lbs TOTAL DRINKS TIME FROM 1st TOTAL DRINKS DRINK 1 2 3 4 5 6 7 8123456781234567812345678 1 hr 2 hrs 3 hrs 4 hrs SHADINGS IN THE CHARTS ABOVE MEAN 01 04 Seldom illegal 150 to 169 lbs TOTAL DRINKS 05 09 May be illegall 05 09 Illegal if under 18 yrs old 230 lbs up TOTAL DRINKS 10 Up Definitely illegal Use this bar graph to answer the question The following statement is included with the graph There is no safe way to drive after drinking These charts show that a few drinks can make you an unsafe driver They show that drinking affects your BLOOD ALCOHOL CONCER BAC The BAC zones for various numbers of drinks and time periods are printed in white gray and red HOW TO USE THESE CHARTS First find the chart that includes your w example if you weigh 160 lbs use the 150 to 169 chart Then look under Total Drinks at the 2 on this 150 to 169 chart Now look below the 2 drinks in the row for 1 your BAC is in the gray shaded zone This means that if you drive after 2 drinks in 1 hour you could be arrested In the gray zone your chances of having an accident are 5 time you had no drinks But if you had 4 drinks in 1 hour your BAC would be in the red shaded area and your chances of having an accident 25 times higher Suppose that you weigh 115 pounds and that you have four drinks in 3 hours If you then drive how much more likely are you to have an accident than if you had refrained from drinkin times

Determine whether or not the sentence is a statement It takes more calories to eat a piece of celery than the celery has in it initially Is the given sentence a statement A No because the sentence can be both true and false simultaneously B Yes because the sentence is always true C Yes because the sentence can be either true or false but not both simultaneously OD No because the sentence is always false

6 23 Portfolio beta and security market line You own a portfolio consisting of the x stocks below MyLab STOCK OR SECURITY 1 2 4 5 PERCENTAGE OF PORTFOLIO 20 30 15 25 10 C BETA 1 00 0 85 1 20 0 60 1 60 The risk free rate is 3 percent Also the expected return on the market portfolio is 11 percent EXPECTED RETURN 12 8 12 7 16 a Calculate the expected return of your portfolio Hint The expected return of a portfolio equals the weighted average of the individual stocks expected returns where the weights are the percentage invested in each stock 1 10

Macmillan Learning Solve the factored equation 12 sin x 6 Give all answers in the form t 2kx where t is in the interval 3x 1 1 Give your answer in the form of a comma separated list if needed Express numbers in exact form Use symbolic notation and fractions where needed Use k to represent any integer x

For each function below identify the Slope and Vertical Intercept Write your numerical answers as whole numbers or reduced fractions Write your intercepts as ordered pairs Write DNE if a slope or an intercept Does Not Exist Function Slope 6y 2x 6 I y 7 7 8x y 9 y 10 50 x DNE 618 I Vertical Intercept DNE 0 0 OT

A company begins advertising a new product and finds that after t weeks the product is gaining customer recognition at the rate of 9t2 In t thousand customers per week for t 1 Find the total gain in recognition from the end of week 1 to the end of week 6 Round your answer to the nearest whole number thousand customers

Suppose that the velocity v 1 in m s of a sky diver falling near the Earth s surface is given by the following function where time t is measured in seco v 1 53 1 e 0 161 Find the velocity of the sky diver after 3 seconds and after 6 seconds Round your answers to the nearest whole number as necessary Velocity after 3 seconds r m s Velocity after 6 seconds m s

An agent s implied authority to perform any act reasonably necessary to execute express authority is called authority express customary O apparent incidental

Due to random variations in the operation of an automatic coffee machine not every cup is filled with the same amount of coffee Assume that the mean amount of coffee dispensed is 8 ounces and the standard deviation is 0 5 ounce Use the 68 95 99 7 rule to complete the following a What percent of the cups should have at least 8 ounces of coffee b What percent of the cups should have less than 7 5 ounces of coffee a Approximately of the cups should have at least 8 ounces Type an integer or a decimal

Differentiate y log5 x x d 6 log 5 x x

Drag the appropriate curve to show the initial change to the short run economy as a result of an extensive wildfire in California using the aggregate demand and supply graph To refer to the graphing tutorial for this question type please click here Price level P LRAS1 SR Real GDP Y

Consider the logarithmic statement below Identify the base Base Identify the exponent Exponent Identify the argument of the logarithm Argument log7 16 807 5 Express log7 16 807 5 in exponential form Exponential Form

3 Find the exact value of the trigonometric expression 150 b 4 tan 5T Pl CSC 2

IJ Exerc Expand the following logarithms Use either the power rule product rule or quotient rule 1 log 95 2 log 21 3 l gs 5 log xy 7 log3 5y Expand 2 9 logs 2 11 log x y 13 log 15 log 2x5 4a 4 log2 6a 6 logs A 8 log 10 log 12 logs E 8 16 109 14 log 9x3 9x 18 Ion 3 2