Questions on Algebra: Exponent and logarithm as functions of power answered by real tutors!

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Question 1033051: Real world applications of exponential & logarithmic functions in the field of space exploration...
Please help, I don't know how to answer this question...I tried searching up some, but nothing came up related to the topic...

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Question 1033178: log3 9x
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Question 1033407: An astronaut r thousand miles from the center of the earth weighs 2880%2Fr%5E2 lbs, and the surface of the earth 4000 is miles from the center.
(a) If the astronaut is h miles above the surface of the earth, express r as a function of h.
r=


(b) Express the astronaut's weight w in pounds as a function of h.
w=

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Question 1033454: What is 5x - x^2. Also read as 5x minus x to the power of 2, My calculator says it is -50 but I am just not sure about that answer
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Question 1033473: Please help, I am very stuck, and it's a 3 part question:
Poiseuille's Law gives the rate of flow, R, of a gas through a cylindrical pipe in terms of the radius of the pipe, r,, for a fixed drop in pressure between the two ends of the pipe.
(a) Find a formula for Poiseuille's Law, given that the rate of flow is proportional to the fourth power of the radius.
Use k as the constant of proportionality.
R=
(b) If R= 550cm3/sec in a pipe of radius cm for a certain gas, find a formula for the rate of flow of that gas through a pipe of radius r cm.
R=
(c) What is the rate of flow of the gas in part (b) through a pipe with a 7 cm radius? Round your answer to two decimal places.
R= ___ cm3/sec

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Question 1033803: X^2+4x+c Find c
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Question 1033854: log(6x+1)+logx=2
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Question 1033951: 4^2x+7=32^x+3

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Question 1034221: Convert 5log5^x = y to logarithmic form.
A) log5x = y
B) log5y = x
C) log5x = y5
D) log5x = log5y
i need help anwserng this question.

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Question 1034277: Write an exponential function y=ab^x for a graph that includes the given points. (4,8), (6,32)
Please explain how you got the answer

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Question 1034277: Write an exponential function y=ab^x for a graph that includes the given points. (4,8), (6,32)
Please explain how you got the answer

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Question 1034503: How do you expand this?
ln(ab^6)^4
I wasn't sure if it would be ln(a^4)+6ln(b^4)

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Question 1034507: how do you solve this equation?
-9.2e^x-7=-94

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Question 1034597: log3 (x + 3) = 2
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Question 1034578: What is the solution of: Log2X + Log2(X-12)=6
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Question 1034598: you have $75 and invest it into an account that gives 2.5% annual interest and compounds continuously. How much longer would you invest if you wanted to quadruple your money instead of doubling it?
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Question 1034598: you have $75 and invest it into an account that gives 2.5% annual interest and compounds continuously. How much longer would you invest if you wanted to quadruple your money instead of doubling it?
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Question 1034599: by how much would you have to decrease the hydrogen concentration if you wanted to raise the pH from 4.5 to 6?
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Question 1034782: Please, graph of t(x)=log(base 2)(x+3)-1
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Question 1034778: t(x)=log(base 2)(x+3)-1
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Question 1034772: log(x)^log(x) = 506
Please show how one would solve for x?

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Question 1034772: log(x)^log(x) = 506
Please show how one would solve for x?

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Question 1034818: a rectangle with a diagonal of length 13 has an area of 60. Find the dimensions of the rectangle.
Please explain.

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Question 1034816: solve log3 |2x-11|=5
please explain

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Question 1034832: The student enrollment of East End High School was 1,250 students in 1990 and increased at a rate of 10% per year until 2004. From 2004 until 2010, the enrollment increased by 6% each year.
Approximately how many students were enrolled at East End High School in 2010?
A. about 8,409
B. about 3,524
C. about 5,282
D. about 6,732

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Question 1034821: Nicole invested a certain amount of money for one year and earned $78 in interest. Jon invested $260 more at an interest rate that was 1% less than Nicole, but earned the same amount of interest. Find Nicole's principal and interest rate.
please explain.

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Question 1034821: Nicole invested a certain amount of money for one year and earned $78 in interest. Jon invested $260 more at an interest rate that was 1% less than Nicole, but earned the same amount of interest. Find Nicole's principal and interest rate.
please explain.

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Question 1034972: Ln 16-ln 8
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Question 1035044: Find an exponential function of the form f(x) = ab x that passes through the points P.
and Q.
(a) P=(-1,4) and Q=(2,32) (b) P=(-2,32) and Q=(1, 1/2)



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Question 1035074: Given function is 2(raise to the power of 1+2x) - 5(2x)= -2
The answer is -1, 1. Please explain and show to me how to get the answer. pls.

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Question 1035074: Given function is 2(raise to the power of 1+2x) - 5(2x)= -2
The answer is -1, 1. Please explain and show to me how to get the answer. pls.

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Question 1035219: Logarithmic Equation. What is the solution set of the function
log(base 5) x + log(base 5) (4x+1)= 1. Pls.

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Question 1035219: Logarithmic Equation. What is the solution set of the function
log(base 5) x + log(base 5) (4x+1)= 1. Pls.

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Question 1035219: Logarithmic Equation. What is the solution set of the function
log(base 5) x + log(base 5) (4x+1)= 1. Pls.

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Question 1035269: 2x^2Inx - 5xInx = 12Inx
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Question 1035270: 8x^2Inx - 6xInx = 9Inx
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Question 1035413: Between the start of 2005 and the end of 2009, the number of Facebook users can be modelled by the exponential equation u=0.43x(3.17)^t where u is the number of users in millions and t is the number of years since the start of 2004 (1<=t,6). So after 1 year (t=1) there are 1.4 million users (to 1 dp)
Find the number of years in which the exponential model predicts that the number of users would first reach 200 million.
I believe I have worked correctly that year 2 = 4.3 and year 3 = 13.7 but I don't know a 'quick' way to reach 200 million
Thank You

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Question 1035675: Please help me with this problem. I have tried it over and over and the answer I keep coming up with is 18000.
$3000 is deposited in an account that pays 5% annual interest for 10 years. How much more would be in the account if the interest were compound continuously rather than quarterly?

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Question 1035676: Please help me and show work. Thanks
$800 is deposited in an account that pays 9% annually interest compounded annually. Find the balance after 4 years.

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Question 1035882: please help me I never and still isn't good on doing these problems. Thanks in advance.
How much you must deposit in an account that pays 6.25% interest, compounded annually to have a balance of $700.00 after 2 years.

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Question 1035882: please help me I never and still isn't good on doing these problems. Thanks in advance.
How much you must deposit in an account that pays 6.25% interest, compounded annually to have a balance of $700.00 after 2 years.

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Question 1035884: Please help never understood how to do these problems. Thanks in advance
If you put 2000 an interest bearing account is compounded quarterly(4 times a year)at 6%, how long will it take for your money to triple?

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Question 1035884: Please help never understood how to do these problems. Thanks in advance
If you put 2000 an interest bearing account is compounded quarterly(4 times a year)at 6%, how long will it take for your money to triple?

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Question 1035880: log2(x8y4/z6)

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Question 1036038: 2^3x+1=3^x-2
I cant figure out how to exactly set up this problem, so you csn help me out I woul really appreciate it.
So far I have 3log2+log2=xlog3-2log3

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