Logarithms Questions and Answers

May 31 6 29 18 PM Solve for a positive value of x log 81 2

A composite solid consists of a rectangular block of lightweight concrete and a triangular wedge of steel with dimensions as shown The rectangular block has a 2 ft radius circular hole drilled through its full depth perpendicular to the front and back faces Assume densities Vc 125 lb ft and ys 493 lb ft Note carefully the coordinate system shown Using this coordinate system determine the location of the Z centroid and enter your answer in units of ft Remember to show all your work including the strategy used equations and calculations on your handworked file to receive full credit I 9 ft 6 ft Lightweight Concrete 125 lb ft 4 ft y Steel 493 lb ft 2 ft 4 ft

show that f x 2 4x x 2 when g f x x 2 and g x 2 f x 2

Find all value of b such that x y Is a solution to system xy bb logb xlogby logb ylogbx 4b4

Ger ek say lar kumesi zerinde tahimilt ve g fonksiyonlar i in f g x x 4x 5 g x x a f 0 2 oldu una g re a ka t r 1 A 2 B C 1 D 3 E 3

90 AD 10 73 10 8 642 2 y up of O NO 6 8 10 Direction of opening Sign of 2nd differences Equation of Axis of Symmetry Coordinates of vertex Max or Min Value

Rewrite the logarithmic equation in exponential form log 49 x 0 0 Hint

Algebra Consider K with density function G k such that G 0 0 and G k 1 g k and z k be a nonnegative monotonic function such that E x K exists Show that E z K z 0 1 G k z k

Find the median of the data in the box plot below 0 pencils 2 4 Number of pencils in each student s desk 6 8 10 12 H 14

1 Use Mathematical Induction to show that that the solution to the recurrence relation with base condition is n T n aT 1 b T 1 c T n callogn

Which expressions are equivalent to the one below Check all that appl log 1 log5 25 A 2 log7 7 B 5 7 C 1 D 0

Solve the initial value problem 5x x 3 dx x 1 y 1 Y 1 5 2 dy 2 Begin by separating the variables Choose the correct answer below A y 1 dy OB 5xx 3 x x 1 O C dy 5x x 3 dx x x 1 y 1 dx x x 1 5x x 3 D The equation is already separated 1 dy dx y 1 The solution is Type an implicit solution Type an equation using x and y as the variables

20 We have a sample of 100 g of caesium The half life of caesium is 30 years How much of the sample will remain after 100 years to the nearest tenth of a gram O 9 7 g O 9 9 g 9 8 g O 9 5 g O 9 6 g

The given graph shows the function s x 2 log x 3 2 5 1 2 A 2 E B 4 4 5 6 8 5 F C

g Find the value of 5 0g 25 h Express log 8 log 5 log 2 as a single logarithm

se properties of logarithms to condense the logarithmic 3 log x 2log ogx 2log z

An abandoned building s value is 230 0 95 t thousand dollars When will Etienne be able to buy the building with his savings account which has 180 000 at year t 0 and is growing by 11 per year Round your answer to three decimal places

Consider the function g x log x 1 The domain of g is the interval from Choose one negative one to infinity negative infinity to infinity negative infinity to zero one to infinity zero to infinity and the x intercept is Choose one 1 1 2 0

The population of a country is 8 million and growing at 2 13 per year What will the population be in x years

log 2 4 The answer format in lowercase characters is log number

equation below It may be helpful to convert the equation into exponential form Write answer as an integer or reduced fraction 3 logg m 10 7 m

4 log 6 3 log x Olog 4 6 3x Olog 4 6 3x O log 6 Olog 4 6 lg 64

Rewrite each of the following equations Make sure to preview each answer a Rewrite 5 25 as a logarithmic equation b Rewrite log 0 001 3 as an exponential equation

Find the logarithm log 100 000

2 2 pts Graph the function h x log x 1 using transformation starting from y 10x Use at least 3 points Domain Range x Intercept Asymptote H 11 10 9 8 81 7 6 5 4 3 6 0 11 x

logs r 9 loger O loge O loge O logs F 9 19 2r VF 9 O 1086 V P D Question 13 12 2 5 pt Solve the logarithmic equation Be sure to reject any value that is not in the domain of the code o original logarithmic expressions Give the exact answer log3x log4 log x 3

What is the result of a general election O it determines which candidate has been elected to office O the candidate for each political party is selected candidates receive money to use for campaign spending the people decide if the government official should be removed or remain in offic

2 63 DETAILS Find an equation for the conic whose graph is shown DETAILS 5

The energy E released by an earthquake is given a Find the earthquake s magnitude b Find the earthquake s intensity E 1016 4 joules a The earthquake s magnitude is Type an integer or a decimal b Select the correct choice below and if necessary fill in the answer box to complete your choice Type your answer using exponential notation OA 1 10 OB I lo O c 110 OD 1 10

The function f x 18 0 955 models the percentage of surface sunlight f x that reaches a depth of x feet beneath the surface of the ocean The figure shows the graph of this function Use the function to determine at what depth to the nearest foot there is 1 of surface sunlight How is this shown on the graph of f Intensity 2 20 40 60 80 Depth At what depth is there only 1 of surface sunlight feet Do not round until the final answer Then round to the nearest whole

Suppose Set A contains 36 elements and the total number elements in either Set A or Set B is 103 If the Sets A and B have 10 elements in common how many elements are contained in set B Answer elements Question Help 1 Video 1 7 Video 2 Mercars instructor

You are now viewing the questions you held earlier Please submit an answer or pass Which of the following is the equation of the line that is parallel to y 2x 8 and goes through point 4 1 y x 1 y 2x 9 y x 3 y 2x 7

Let log A 6 log B 2 and log C 5 Evaluate the following logarithms using logarithmic properties 1 log 2 log AB B C3 3 log BAC

Suppose the merger of two firms Heinz and Beech Nut will reduce the price elasticity of demand for each firm s product from 2 to 1 For each firm the average cost of production is constant at 3 per unit Suppose Heinz initially has a price of 10 at which they sell 100 units and is considering raising the price to 11 Compute the profit with the new price of 11 after the merger elasticity 1

The Richter scale measurement for an island earthquake of 2007 was 6 9 Find the intensity of this earthquake as a multiple of lo The intensity of the earthquake was approximately lo Round to the nearest whole number as needed

he duration t in minutes of customer service calls received by a certain company is given by the following probability density function Round your answers to four ecimal places f t 0 5e 0 5t t20 a Find the probability that a call selected at random lasts 2 minutes or less 0 6321 b Find the probability that a call selected at random lasts between 5 and 10 minutes 0753 c Find the probability that a call selected at random lasts 2 minutes or less given that it lasts 5 minutes or less 9179 X

Part 1 of 2 The amounts in dollars paid by 20 students for textbooks during the fall term are given on the right Fill in the correct frequencies in the frequency table based on the data Interval Frequency 10 19 99 20 29 99 30 39 99 40 49 99 50 59 99 60 69 99 O Points 0 of 1 8 points

14 Complete the table h 0 1 0 01 0 001 0 0001 0 0001 0 001 0 01 0 1 eh 1 h

Exercise 2 Exponential functions and equations For the function h x 2x 1 5 1 Find its graph domain and range Dom Range II Solve the equation 0 2e 1 5 10 5 10 0 10 5

Solve 6 sin 5 4 for the four smallest positive solutions

55 Which of the following items Multiple Choice O O O Office equipment Prepaid rent Office supplies Merchandise Inventory

Find the radius of the circle in the figure to the right 3 5 19t

Sketch the graph of each function Plot a aymptote 1 f x log x 1 2 8 6 4 2 8 ob 6 21 2 y O 8 x

coin sold for 215 in 1980 and was sold again in 1989 for 447 Assume that the growth in the value V of me collector s item was exponential Round to the nearest tenth Find the amount of time after which the value of the coin will be 3030 years poprost tenth

A radioactive substance decays exponentially A scientist begins with 140 milligrams of a radioactive substance After 17 hours 70 mg of the substance remains How many milligrams will remain after 29 hours mg Give your answer accurate to at least one decimal place Submit Question

3 5 6 Show that the second order differential equation d u dx du a x b x c x u d x dx for a x 8 with u a A and u B B can be solved by an algorithm similar to the Thomas algorithm Set du dx and determine equations for p x and q x D p x u q x

ind the y coordinate of the inflection point for the following logistical growth function 5000 9 45e 1 38t s t coordinate of the inflection point

A biologist goes out into the Organs and finds the population of hares to be 5 615 The population doubles every 15 years What is the initial population of rabbits

Homework The population of a coun of the country in billions

4 10 IE to indicate o If no solution exists enter DNE Enter your answer in INTERVAL notation Use U to indicate a union oo