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

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Question 169646: Will you please help me with the following problem? I need to express Log base three of twenty seven to the negative third power as a product and then simplify it. I have tried writing it as an exponential equation instead but it didn't go so well. I got stuck once I changed it into Three to the x power is equal to twenty seven to the negative third power. Am I even on the right track? Please help!
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Question 169643: I really need your help evaluating this- log base four of one sixteenth. I am supposed to use mental math and I have no Idea how to do this. Would you please help me? (Sorry about spelling it out, I don't know how to type numbers with exponents or bases.)
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Question 169650: The graph of an exponential function is given. Select the function for the graph from the functions listed.
There is a graph attached to the problem, but I was unable to load it. Start on the x axis at -1,0 bending up to the y axis (1,1). If you would like me to email you the graph, I can.
The following are answers that are avaiable;

f(x) = 4x + 2
f(x) = 4x - 2
f(x) = 4x + 2
f(x) = 4x

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Question 169950: I'm struggling with how to solve this problem. I just don't know what to do?
N(2)= 7000/1+999e^-2
How do you solve this?

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Question 169185: Please help.
Solve:
a) 4^x-6 = 16^x
===================
b) e^-2x = 0.3
Thank you.

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Question 169185: Please help.
Solve:
a) 4^x-6 = 16^x
===================
b) e^-2x = 0.3
Thank you.

Click here to see answer by jim_thompson5910(35256) About Me 

Question 169999: Please help me with:
Simplify; 1ne^-3x-4
Thank you.

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Question 170000: Please help.
Construct and simplify the difference quotient for f(x)= x^2-x.

Thanks

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Question 170051: Please help me with:
The speed of the current in a river is 2mph. Jay travels 20 miles upstream and then 20 miles downstream in a total time of 5 1/3 hours. Find the speed of the boat.
Let s be the speed of the boat.

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Question 170129: I do not understand how to solve this problem.
N(2)= 7000/1+999e^-2
How do you get the answer? I've got the answer. It is 7000/1+(135.199947953)
I don't know what to do to get it . I'm stuck. Thank you for helping me.

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Question 170160: I just can't figure out what i'm doing wrong.
N(10)=10000/1+999e^-10

How do you solve this problem?
Can I get help with this problem,too.
P(3636)=(404)3^t/2
How do you solve this?

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Question 170173: Explain the relationship, if any, among the following equations.
16^2=x and 16=logx^2

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Question 170173: Explain the relationship, if any, among the following equations.
16^2=x and 16=logx^2

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Question 170173: Explain the relationship, if any, among the following equations.
16^2=x and 16=logx^2

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Question 170020: Please help me with this problem:
If (-10,10) is on the graph y=f(x), what point do you know is on the graph of
f(1/2(x))?
Thank you.

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Question 170206: Can someone please explain how to answer the following 2 problems? Any assistance is greatly appreciated!
The population of a country doubled in 100 years. What was the exponential growth rate?
and
Solve
ln square root of x-2=1

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Question 170203: Can someone show me how to solve the following 2 questions:
4^x-6=16^x
and
e^-2x=0.3

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Question 170256: Can someone please explain how to solve the following 2 problems. Any assistance you can provide is greatly appreciated!
the log of (x+5), base 2 + the log of (x-1), base 2 =4
and
the log of 6, base 36 = x

Click here to see answer by Earlsdon(6294) About Me 

Question 170275: Can someone please explain how to solve the following problem. Your assistance is greatly appreciated!
Express in terms of sums and differences of logarithms
log square root of x^4/yz

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Question 170275: Can someone please explain how to solve the following problem. Your assistance is greatly appreciated!
Express in terms of sums and differences of logarithms
log square root of x^4/yz

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Question 170404: A bacteria culture starts with 120 bacteria and after three hours the population consists of 200 bacteria. assuming that the culture grows exponentially, find the poplation after 5 hours.
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Question 170591: simplify e^2e^5
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Question 170666: I need help getting started the equation is 2^3x-4=64
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Question 170938: hello, I really need some help with this problem:
-5y^4(y^5)^2
_____________
15y^7(y^2)^3
Thanks so much in advance

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Question 170938: hello, I really need some help with this problem:
-5y^4(y^5)^2
_____________
15y^7(y^2)^3
Thanks so much in advance

Click here to see answer by checkley77(12844) About Me 

Question 170952: I need some help with this problem:
Simplify (3y^8/2zy^2)^4
Thanks on advance

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Question 170952: I need some help with this problem:
Simplify (3y^8/2zy^2)^4
Thanks on advance

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Question 171265: Could you please help me with this question:
Two people with the flu visited a college campus. The number of days T that it took for the flu virus to infect n people is given by
T = -1.43 ln(10,000 - n/4998n).

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Question 171325: My Toyota Avalon was purchased for $27,500 in 1997. It has been decreasing in value at an average rate of 15% annually since then. When is its approximate value now?
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Question 171323: The cost of attending college has been rising at an average increase of 7% for the past ten years. How much will college that now costs $10,368 for room, board, tuition and fees cost two yearsfrom now?
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Question 171326: (3.14r^3)(3r)^2
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Question 171742: This is the last part of my homework and I am completely stumped on how to do exponents and logarithms. Please help me. It is 12:25am EST and I can not get this. Help me please!
1. A cell divides into two identical copies every 4 minutes. How many cells will exist after 3 hours?
2. The level of thorium in a sample decreases by a factor of one-half every 4.2 million years. A meteorite is discovered to have only 7.6% of its original thorium remaining. How old is the meteorite?

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Question 171741: I am having trouble solving these three questions involving logarithms and exponents. Any help with solving these would be appreciated. Thank you!!!!!
1. Do exponential functions only model phenomena that grow, or can they also model phenomena that decay? Explain what is different in the form of the function in each case
2. True or false: The function "f(x) = 3x" grows three times faster than the function "g(x) = x". Explain.
3. What are the asymptotes of the functions "f(x) = 3x" and "g(x) = log52x"?

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Question 172076: Dear tutors, I am desperate, I need help plotting and graphing these questions. Any assistance will be greatfully appreciated! Thank you!
Plot the graphs of the following functions and graph.
1. f(x)=7x
2. f(x)=4x - 3
3. f(x)=(1/5)x
4. f(x)= log3x

Click here to see answer by Alan3354(69443) About Me 
Question 172076: Dear tutors, I am desperate, I need help plotting and graphing these questions. Any assistance will be greatfully appreciated! Thank you!
Plot the graphs of the following functions and graph.
1. f(x)=7x
2. f(x)=4x - 3
3. f(x)=(1/5)x
4. f(x)= log3x

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Question 172169: completing squares
directions: find the value of c that makes the expression a perfect square trinomial. Then write the expression as the square of a binomial.
question: x2 + 10x + c


my work: 10
-- = 5 then (5)2= 25 then x2 + 10x + 25 = 0 then (x + 5) 2 = 0
2


then I square rooted both sides which = x + 5 = 0 x = + 5
-5 -5 -
-----------
Well I don't know if I did it right someone please help.

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Question 172514: (29.3)^4x-1 = (17.3)^5x+2
Solved without the use of a calculator

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Question 172528: if log base a of x equals c and log base b of x equals c, what is log base ab of x equal to?
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Question 172663: True or false: The function "f(x) = 3^x" grows three times faster than the function "g(x) = x". Explain
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Question 172703: if "b" is an integer and 3.2.*10(to the "b" power) is a number between 500 and 5,000, what is the value of "b"?
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Question 172894: can you please explain the answer to i^49? I factor out 13*3, but cannot resolve the remaining terms...thanks
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Question 172894: can you please explain the answer to i^49? I factor out 13*3, but cannot resolve the remaining terms...thanks
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Question 172875: 1/3 log 5 12x=2


solve equation and find extaneous solutions

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Question 172993: Please solve the exponential equation:
%285x%5E2%2F5%5E%283x%29%29=625

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Question 173000: How do I evaluate the functions for the values of x given as 1, 2, 4, 8, and 16 and then describe the differences in the rate at which each function changes with increasing values of x? This is like totally a different language for me, please help!!!!
1. f(x) = 5x - 3
2. f(x) = x2 - 3x + 2
3. f(x) = 2x3 + 7x2 - x - 1
4. f(x) = 10x
5. f(x) = ln x

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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, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760, 5761..5805, 5806..5850, 5851..5895, 5896..5940, 5941..5985, 5986..6030, 6031..6075, 6076..6120, 6121..6165, 6166..6210, 6211..6255, 6256..6300, 6301..6345, 6346..6390, 6391..6435, 6436..6480, 6481..6525, 6526..6570, 6571..6615, 6616..6660, 6661..6705, 6706..6750, 6751..6795, 6796..6840, 6841..6885, 6886..6930, 6931..6975, 6976..7020, 7021..7065, 7066..7110, 7111..7155, 7156..7200, 7201..7245, 7246..7290, 7291..7335, 7336..7380, 7381..7425, 7426..7470, 7471..7515, 7516..7560, 7561..7605, 7606..7650, 7651..7695, 7696..7740, 7741..7785, 7786..7830, 7831..7875, 7876..7920, 7921..7965, 7966..8010, 8011..8055, 8056..8100, 8101..8145, 8146..8190, 8191..8235, 8236..8280, 8281..8325, 8326..8370, 8371..8415, 8416..8460, 8461..8505, 8506..8550, 8551..8595, 8596..8640, 8641..8685, 8686..8730, 8731..8775, 8776..8820, 8821..8865, 8866..8910