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Tutors Answer Your Questions about Exponential-and-logarithmic-functions (FREE)
Question 28781: Hi, I have been going over this more time then you know. I need to use the laws of logarithms to express logarithm in base 2 of 6 minus logarithm in base 2 of 3 plus 2logarithm in base of 2 sqrt 8.
This is what I have,
Original equation
= logarithm in base 2 of 6 - log in base of 2 of 3 + log in base of 2 of 8^1/2
= SAME + log in base of 2 of 2^3 (base of two and 2 to the power of cancel out)
=Same as top + log3
=log in base of 2(6)(3) - log3
=log in base of 2 = (18/3)
log2 = 6
I really hope this makes sense, because I'd really appreciate help. I'm not sure if I did this right, it kind of seems like I haven't so thats why I'm here double checking. Thank you for your time.
Click here to see answer by longjonsilver(2297)   |
Question 29022: I have to solve N(t) =N_0(2)^t/d for t using logarithms.
This is what I have and I'd really appreicate some help on it.
logN(t) = log(N_0(2)^t/d)
logN(t) = t/d log(N_0)(2)
t/d = log(N_0(2)) / log(N(t)
t = log(N_0(2)) / log(N(t) * d
Is this right? Thank you.
Click here to see answer by venugopalramana(3286)  |
Question 29563: Okay, well I am in Agebra 2. I have never really understood the concepts, as much as I try. I take all notes in the class, and how they come up with these numbers, I have no clue.
I guess one of the biggest problems I am having are the "extraneous solutions".
I don't like the answers givien to me, but I do like knowing how to do them and the steps... ONe of them problems is
The square root of x +12 = x.
From what I understood from my teacher.. I waould trop the x+12 down like
x + 12 = x
-x -x
12 ? Square root of 12 =3.50??
What did I do wrong?
Another problem is
(3x-8)^1/2=5
3x-8^1/2 =5 I dropped the 3x-8
+8 +8 I added 8 to both sides
3x^1/2=13 and I don't know what to do? Divide by three? Then if I do that? what happesn to the the power?
Any help of what I am doing wrong, would be greatly appreciated.
Click here to see answer by bmauger(101)  |
Question 30189: A rocket has a mass ratio of 24 and an exhast velocity of 2.5km/s. Determine the minimum firing time for a stable orbit 300km above Earth.
Use the formula: v = -0.0098t+c ln R
I tried to plug in the information into the formula, but there was a missing variable. This is what I got:
V = -0.0098t+2.5ln24
Since we are suppose to find the time, then there is a missing varible: the velocity. Please check over my work. Thank you.
Click here to see answer by longjonsilver(2297) |
Question 30528: I got this problem wrong on a test and rather than telling me what I did wrong, the teacher just wrote the answer as being X = 4. I have been going over it and I can't figure out this problem. Can someone please write this problem out for me so that I can hopefully figure this out?
Solve log (small 3) (2x+1) = 2 for x.
Thanks a bunch!!
Theresa
Click here to see answer by sdmmadam@yahoo.com(530) |
Question 30715: A person's blood has a pH of 7.408 and a bicarbonate concentration of 26.4. Approximate the concentration of carbonic acid in the person's blood. We were given this formula: pH= 6.1 + log10(x/y) where x is the concentration of bicarbonate and y is the concentration of carbonic acid.
Click here to see answer by Nate(3495) |
Question 30861: Here is a doozy, my group and I have been trying to figure this one out for awhile.
Exponential Decay: Water Filtration
As an environmental consultant, you are responsible for the remediation of effluent from a pulp mill. Each hour, a quantity of water containing 500 grams of pollutants is discharged. According to environmental regulations, the contaminent level must be reduced to less than 150 grams before the effluent can be discharged into the local river system. The effluent must pass through a series of filters to reduce the contaminant level to an acceptable value. Each time the effluent passes through one filter, 18% of the contaminants are removed.
We figured out the equation:  . What we can't figure out is how to re-arrange or write an equation to how many filters are required to reduce Cn to less than 150 grams. Can any one help?
My second question is one of the opposite, Exponential Growth:
Two students are saving money for a graduation trip to Asia in 3 years time. George has just sold his car for $3000 and has invested his money in a bond at an interest rate of 5.4% per year, compounded monthly. At the same time, John has invested his part-time job savings of $2700 in a GIC at an interest rate of 6.8% per year, compounded quarterly.
We indentified the equations as: George -  , where t is the number of years of growth.
John -  , where t is the number of years of growth.
**The question we are struggling with is this: How do we re-write or write an equation to express after how many years will the two investments be approximately equal in value?
We can answer both of these by looking at our plotted points or our graphs but we were wondering if there is an Algebraic equation way of expressing them.
Thanks
Melissa
Click here to see answer by acerX(62) |
Question 31655: Question:
Express in terms of logarithms of x, y, and z: log [a] 4xy^5/z^5
Answers:
(1) 4+log[a]x+5log[a]y-5log[a]z
(2) 20+ log[a]xy-5log[a]z
(3) log[a]4+log[a]x+5log[a]y-5log[a]z
(4) log[a]4+log[a]x+5log[a]y/5log[a]z
Please be specific as to which answer is correct. This is a confusing question to me. Thank you greatly.
Click here to see answer by longjonsilver(2297) |
Question 31666: Oh this logarithm problems are killing me :)
Can you help! Write hte logarithm of a single expression:
log[b]6x+4(log[b]x-log[b]y)
(A) log[b] 6x^5/y^4
(B) log [b] 24x^2/y
(C) log [b] 10x/4y
(D) none of these.
Do we even consider the "B" in this expression?
Click here to see answer by mukhopadhyay(490) |
Question 31889: This is a question on a take home assignment, extra credit. Please help!
Find all real solutions to the following equation :
log [2](x+2) +log{2}(x+4) =3
(A) x=0
(B) x=4
(C) x=0, -6
(D) none of these
Thank you for your help!
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
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