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Tutors Answer Your Questions about logarithm (FREE)
Question 91830: The graph of the basic exponential function (y = bx) has two distinctive characteristics:
a) having a y intercept of (0,1), and
b) having a horizontal asymptote of y=0.
Since inverse functions have their domains and ranges interchanged, what impact does this have for the graph of y = logb(x
Click here to see answer by stanbon(26252)   |
Question 91830: The graph of the basic exponential function (y = bx) has two distinctive characteristics:
a) having a y intercept of (0,1), and
b) having a horizontal asymptote of y=0.
Since inverse functions have their domains and ranges interchanged, what impact does this have for the graph of y = logb(x
Click here to see answer by Nate(3495) |
Question 91831: 1. Why does the graph of the basic exponential function
(y = bx, where b>0, and b not 1) lie entirely above the x-axis?
2. Explain the difference between natural logarithms and common logarithms.
Click here to see answer by Nate(3495) |
Question 91932: This is frustrating. I've been working on this problem for too long now. It's a simple problem, but when I asked a tutor at my school for help, she said it was correct when I showed her my answer. I was to evaluate log-base7 7^3. I divided Log7^3 by Log7 and got .8450 Another tutor told me the answer is 2, because 2 divisions are used to get to 1. now I'm lost and trying to figure this out. Which answer is it? This is my last question for the day. :o)
Click here to see answer by kev82(145) |
Question 91993: Write the mathematical definition for a logarithm (i.e. for: logb N).
4. The definition of the log function (y = logb N, where b>0, b not 1) is based on the definition of the exponential function. Explain why you cannot take the logarithm of a negative number. (Why must N be greater than 0?)
Click here to see answer by stanbon(26252) |
Question 92001: Lead shielding is used to contain radiation. The percent of a certain radiation that can penetrate x millimeters of lead shielding is given by r(x) = 100e^-1.5x. What percent of radiation, to the nearest tenth of a percent, will penetrate a lead shield that is 3 millimeters thick?
Click here to see answer by mathispowerful(115) |
Question 92001: Lead shielding is used to contain radiation. The percent of a certain radiation that can penetrate x millimeters of lead shielding is given by r(x) = 100e^-1.5x. What percent of radiation, to the nearest tenth of a percent, will penetrate a lead shield that is 3 millimeters thick?
Click here to see answer by stanbon(26252) |
Question 91829: Ten years ago your friend invested in a plot of land with the idea of eventually building a summer cottage on it. His plan was to place a "nest egg" of $12,000 in a long term Certificate of Deposit which paid 8% interest over a period of 20 years, compounded monthly. At the end of the 20 years, he would use the money to build the cottage.
The problem was the plot had 8 prairie dogs on it 10 years ago when he acquired the ground.
This year he made a count of the prairie dogs and found there were 102 on the same plot! A biologist friend assured him that the prairie dogs were growing exponentially according to the law of natural growth, and something needed to be done.
1. Write the formula for natural exponential growth for this particular prairie dog population.
Hint: Find the "k" value for this population, and put it in your formula.
1. Write the formula for natural exponential growth for this particular prairie dog population.
Hint: Find the "k" value for this population, and put it in your formula.
2. Once you have this formula, predict:
a. approximately how many years from now will the population reach 365 prairie dogs.
b. approximately how large the population will be 10 years from now.
3. Write the formula for compound interest and calculate how much money your friend will have on deposit (in the account described above) after 20 years (10 years from now).
Click here to see answer by ankor@dixie-net.com(6689)  |
Question 92048: The population of the United States tends to grow at a rate proportional to the size of the population. Thus we may represent the population size by the exponential model A(t) = 180e^0.013t, where t is the number of years since 1960 and A(t) is the population in millions. In what year will the population of the United States exceed one billion?
Click here to see answer by Nate(3495) |
Question 92176: A jewelry maker made two purchases. The first purchase, which cost $220, included 50 grams of a silver alloy and 40 grams of a copper alloy. The second purchase, at the same prices, cost $140 and included 25 grams of the silver alloy and 30 grams of the copper alloy. Find the cost per gram of the silver alloy and the copper alloy.
Click here to see answer by scott8148(3382)  |
Question 92210: At a factory, the number of items N that a newly hired worker can assemble per hour can be modeled by the equation N = 14.6 ln(t + 1), where t is the number of weeks after the worker is hired. How many items per hour can the worker assemble after working at the factory for 6 weeks?
Click here to see answer by stanbon(26252) |
Question 92274: At a factory, the number of items N that a newly hired worker can assemble per hour can be modeled by the equation N = 14.6 ln(t + 1), where t is the number of weeks after the worker is hired. How many items per hour can the worker assemble after working at the factory for 6 weeks?
Click here to see answer by ankor@dixie-net.com(6689) |
Question 92490: 1) How many solutions are there for the equation 3x - 11y = 15?
2) How many points are on a line (such as the one whose equation is:
3x - 11y = 15)?
3) Do all the solutions for 3x - 11y = 15 also make 3x - 11y >= 15 true?
4) Does 3x - 11y >= 15 have more solutions than 3x - 11y = 15? Which graph contains more points? Are they not both infinite?
Click here to see answer by stanbon(26252) |
Question 92851This question is from textbook
: 1) Find the domain and explain the answers for each
a) f(t)= 4.5e^t
b) g(x) = log(x+3)
Is the base g? which makes it g = log x+3? throwing up hands pulling out hair
c) g(x) = 2^x
d) g(t)=ln(t-1)
This is driving me nuts. can someone explain this to me in a simple way? This question is from textbook
Click here to see answer by stanbon(26252) |
Question 93147This question is from textbook
: I am in need of great assistance...calling on experts for this pitiful student. I don't get algebra, I don't get it..I don't get it......My mind is flying with variables that I cannot think straight. I have been working on this problem for two days (screaming)....
11.)The formula for calculating the amount of money returned for an initial deposit into a bank account or CD (certificate of deposit) is given by
A = P(1+r/n)^nt
A is the amount of the return.
P is the principal amount initially deposited.
r is the annual interest rate (expressed as a decimal).
n is the number of compound periods in one year.
t is the number of years.
Carry all calculations to six decimals on each intermediate step, then round the final answer to the nearest cent.
Suppose you deposit $2,000 for 5 years at a rate of 8%.
a)Calculate the return (A) if the bank compounds annually (n = 1). Round your answer to the hundredth's place.
b)Calculate the return (A) if the bank compounds quarterly (n = 4). Round your answer to the hundredth's place.
c)Does compounding annually or quarterly yield more interest? Explain why.
d)If a bank compounds continuously, then the formula used is A=Pe^rt
where e is a constant and equals approximately 2.7183.
Calculate A with continuous compounding. Round your answer to the hundredth's place.
e)A commonly asked question is, How long will it take to double my money? At 8% interest rate and continuous compounding, what is the answer? Round your answer to the hundredth's place.
I am totally lost with this. Can someone help me. S.O.S.This question is from textbook
Click here to see answer by checkley75(3666) |
Question 93484This question is from textbook 
: write in exponential form and simplify this is really hard to explian so please try follow along carefully (the little 3)then the sqrt a^5 (then the little 5) then sqrt aThis question is from textbook
Click here to see answer by stanbon(26252) |
Question 93760This question is from textbook
: please help me solve each equation for x.
log(then a smaller then normal 2)x = 2log(then a smaller then normal 2)2 + log(then a smaller then normal 2) 5This question is from textbook
Click here to see answer by Nate(3495) |
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Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510
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