Homework Help

[PacificGreen 1,163]

Anyone who needs help with math, physics, chemistry, or a foreign language can PM me.

[Kivil 1,721]

Welp, I landed myself in English 1 and I am in the 8th grade so that equals advanced for my grade. Well, my Eng 1 teacher gave me an argumentative essay to do and I have no idea how to do them because I forgot over the summer. Can anyone tell me how to do one? Also, how does one explain Conformity vs Individualism in an essay???

[SasQ 1,355]

I've had this annoying question sitting in my head for a year now. I'm right, but no math person I talk to understands why I'm right.

 

First, your calculations are correct and theirs are wrong. You are right on this one.

Their mistake is only at the end, where they go from log_a(2^(7/2)) to 7/2, because this is based on an assumption that a=2, which contradicts their givens. The unknown a cannot be 2, because log_2(2) = 1, not 0.301.

(Also they should add "..." after these numbers, since those are just approximations; the actual numbers are irrational and cannot be expressed in digital form in a finite way).

So the correct answer in their case should be (7/2)*log_a(2) = (7/2)*0.301... = 1.0535..., precisely what you've got in your correct solution.

 

Well, this is just a quick thing I'm doing while at work, but working within parenthesis

log a(squareroot(128))  is the same as

log a (8*squareroot(2)).  If you know that

8*squareroot(2) is 11.31370849 then you know that it comes to

log a (11.31370849) which is

1.05360498448

 

If you planned to take the logarithm from a decimal approximation anyway using your calculator, then you didn't have to split the sqrt(128) into 8*sqrt(2), since both are equal to 11.31370849...   But your calculations in this way bring you nowhere, because now you're left with log_a(11.31370849...) and you don't know which base you need to take this logarithm to, because you don't know a.

Well, you can always guess it (it's pretty easy to guess if you have experience with these numbers), but guessing is not the correct way of solving math problems in schools and engineering. I'm really curious how did you guess that log_a(11.31370849...) = 1.05360498448 ? Unless you simply pressed the "log" button on your calculator and the calculator guessed for you (using the default base 10, which is correct in this case).

 

Since they gave three particular values of log_a as given, but they didn't give a, the correct path of solution is to massage the expression in such a way to somehow get these three logarithms in it, and then use the values they gave you (as @@Knight Hadron properly did).

 

Because log 2 = 0.301 so if it's log a*2 then (a) is 1. Which would actually make the answer the same either way. So unless I misunderstood or misread something, the answer would be 1.054, and a=1

 

This is also wrong. And you would know it if you thought for a while what would it mean to have a logarithm to the base 1. The logaritm gives the exponent of a base for a given power. Every real power of 1 is 1 (you can see it here). You cannot get any other number than 1 this way. The equation 1^x = p doesn't have any solutions in real numbers if p is not 1, and if it is 1, then any x will do. Which means that there is no real logarithm to the base 1 of any real number. In particular, you cannot get 0.301... or 0.845... or 0.903.. or even your own end result this way. Assuming a=1 contradicts the givens.

 

The correct answer is a=10, because:

log_10(2) = 0.301029995...

log_10(7) = 0.84509804...

log_10(8) = 0.903089987...

log_10( sqrt(128) ) = log_10( 8*sqrt(2) ) = log_10(11.31370849...) = 1.053604985...

but the problem was not to find the value of a, but to calculate the answer without knowing it, having only the values of log_a given for some particular arguments.

 

@, if you need some more help with understanding logarithms (not only calculating them by applying known formulas, but also understanding where did the formulas come from and why are they the way they are; what are logarithms anyway and how do they work), then feel free to PM me on that.

 

how does one explain Conformity vs Individualism in an essay???

 

Pretty much the Season 5's premiere

Edited September 9, 2015 by SasQ

[WhiteShadow 18]

First, your calculations are correct and theirs are wrong. You are right on this one.

Their mistake is only at the end, where they go from log_a(2^(7/2)) to 7/2, because this is based on an assumption that a=2, which contradicts their givens. The unknown a cannot be 2, because log_2(2) = 1, not 0.301.

(Also they should add "..." after these numbers, since those are just approximations; the actual numbers are irrational and cannot be expressed in digital form in a finite way).

So the correct answer in their case should be (7/2)*log_a(2) = (7/2)*0.301... = 1.0535..., precisely what you've got in your correct solution.

 

 

If you planned to take the logarithm from a decimal approximation anyway using your calculator, then you didn't have to split the sqrt(128) into 8*sqrt(2), since both are equal to 11.31370849...   But your calculations in this way bring you nowhere, because now you're left with log_a(11.31370849...) and you don't know which base you need to take this logarithm to, because you don't know a.

Well, you can always guess it (it's pretty easy to guess if you have experience with these numbers), but guessing is not the correct way of solving math problems in schools and engineering. I'm really curious how did you guess that log_a(11.31370849...) = 1.05360498448 ? Unless you simply pressed the "log" button on your calculator and the calculator guessed for you (using the default base 10, which is correct in this case).

 

Since they gave three particular values of log_a as given, but they didn't give a, the correct path of solution is to massage the expression in such a way to somehow get these three logarithms in it, and then use the values they gave you (as @@Knight Hadron properly did).

 

 

This is also wrong. And you would know it if you thought for a while what would it mean to have a logarithm to the base 1. The logaritm gives the exponent of a base for a given power. Every real power of 1 is 1 (you can see it here). You cannot get any other number than 1 this way. The equation 1^x = p doesn't have any solutions in real numbers if p is not 1, and if it is 1, then any x will do. Which means that there is no real logarithm to the base 1 of any real number. In particular, you cannot get 0.301... or 0.845... or 0.903.. or even your own end result this way. Assuming a=1 contradicts the givens.

 

The correct answer is a=10, because:

log_10(2) = 0.301029995...

log_10(7) = 0.84509804...

log_10(8) = 0.903089987...

log_10( sqrt(128) ) = log_10( 8*sqrt(2) ) = log_10(11.31370849...) = 1.053604985...

but the problem was not to find the value of a, but to calculate the answer without knowing it, having only the values of log_a given for some particular arguments.

 

@, if you need some more help with understanding logarithms (not only calculating them by applying known formulas, but also understanding where did the formulas come from and why are they the way they are; what are logarithms anyway and how do they work), then feel free to PM me on that.

 

 

Pretty much the Season 5's premiere

 

Wow, I feel dumb

 

You are of course right, I've been out of math for so long I wasn't really paying attention, and saw it as; 

Log(Presuming base 10, as that was how I learned it if there is no stated base) of (the variable (a) times another number). So, by the fact that I know what log 10 of those number's themselves was, (a) would be 1. I thought he was asking how to show that differently, thus I showed him a way of breaking down the multiplied numbers into a different form.

 

Obviously, I need to pay more attention, and or not do math

[SasQ 1,355]

Wow, I feel dumb

No need to Everyone makes mistakes. Dumb people simply cannot admit it because they deliberately refuse to learn from their errors. (I'd say they choose to be dumb). And you're certainly not one of them.

 

Log(Presuming base 10, as that was how I learned it if there is no stated base)

Yeah, there is a huge problem with math symbols even to this day, due to different definitions and symbols being used at the same time. For example, I used to assume base 10 too when I see "log" without any base explicitly stated. But WolframAlpha.com decided to assume the natural base, "e", for their "log" function which is veeery confusing. Here where I live, natural logarithms are symbolized as "ln" (from Latin "logarithmus naturalis").

 

Same goes with binary logarithms (base 2) used in computer science, because they use "log" instead of "log_2" often as well, assuming that "in computer science it is always base 2" I was taught to use "lg" symbol for binary logarithms, or state "log_2" explicitly.

 

But even bigger problem is with the radical symbol used to denote roots. In 17th century there was no problem, because no one treated negative numbers seriously, not to mention imaginary numbers. So there was only one "root" for every number: the positive one. But what is the square root of 4 when you already know that there are negative numbers? Then you know that 2*2=4, but also (-2)*(-2)=4, so there are actually two square roots of 4: one positive, and one negative! (+2 and -2). But if a mathematician wants the square root operator to be a function (which is a useful property to have), it cannot have two different values. So there is a big disagreement between mathematicians about what should the radical symbol mean.

 

One group insists that the radical symbol should mean just the principal root (the first one to be found, usually a positive real number). This has the advantage that you can denote the negative root by using the positive one with a minus sign before it. Otherwise how would you denote the two square roots of 2? With the radical symbol being reserved for primary root, you can just write root(2) and -root(2) to denote both possible square roots of 2. It gets more complicated, though, when complex numbers come into play, because the concept of positive and negative numbers and being opposite, greater, or smaller, doesn't apply there anymore.

But if the radical sign is used for the results, how to denote the operation?

 

There is another group which uses the radical sign for denoting the operation of taking roots, or finding all roots of a number. They call it "algebraic root" and oppose it to "arithmetic root", but the opposition is simply a convention, because the notation is the same for both, which again is confusing, because when you see a radical sign, how can you know which definition you should use?

They won't let you go all happy-go-lucky about that though – if you make any mistake in your calculations, they will say that you're dumb and don't know the basic mathematics because you confused the algebraic root with arithmetic root. Been there, had it done to me.

 

I see that the problem with the radical symbol results from mixing two different things together: the operation of taking or finding a root of a number (which can result in multiple answers), and the root itself which is always a single number (just one out of many possible answers). The problem is that mathematicians cannot decide which one of these notions to ascribe to the radical symbol. Which often leads to confusion and mistakes. Even the great Leonhard Euler fell into that trap.

 

Personally I use fractional powers to denote the operation of finding roots, and the radical symbol to denothe these particular roots (particularly, the principal root). So far this distinction in notation seems to be consistent and let me avoid many mistakes, so perhaps it should be applied more widely. But mathematicians are not very willing to listen someone who doesn't have a PhD in mathematics If you say something they're not accustomed to, they will rather call you an ignorant than listen to you.

 

of (the variable (a) times another number).

OK I get it now. So your mistake was justified.

Especially that it is hard to do math without being able to use sophisticated formatting.

This forum allows subscript and superscript though, so perhaps I should correct my post to use it, and the original poster should do it as well?

 

Obviously, I need to pay more attention, and or not do math

When doing math, attention is needed. But you can become an expert only by practicing in the right way, doing mistakes and learning from them. So you shouldn't stop doing math just to avoid mistakes. It's a shame that our educational system convinces us that it's better not to do something that making an error. But that's basically what they teach us by punishing us for our mistakes with bad grades.

Edited September 10, 2015 by SasQ

[TheFizzyFilly 51]

I work in education and also have a degree in English if anypony ever wants my help!! I have also tutored in math 

[Cosmik Vek 764]

Please dismiss this post as I'm "done" with the work

Edited September 12, 2015 by Cosmic V0rtex

[LeonShi500 155]

Wow, so many people offering homework help here, almost more people offering aid than actually requesting it. XD

I never really needed homework help for math back in the day, but when It came to learning the more difficult side of logarithms, I bet this place would have come in handy. 

[SasQ 1,355]

Wow, so many people offering homework help here, almost more people offering aid than actually requesting it. XD

It was once a separate thread for the offers of tutoring and knowledge exchange. But someone decided to merge it with another thread where people were asking for help with their homeworks. In my opinion, this was a very bad idea, because tutorial exchange is something very different than helping someone with their homework or asking for solutions to particular problems. Now it's all mixed up and the homework help questions basically took over the tutorial exchange thread, making it no longer useful :okiedokielokie: But oh well, looks like this is how the new forum staff likes to view this forum now...

 

when It came to learning the more difficult side of logarithms

Logarithms are actually pretty easy if only they're taught correctly, from the historical point of view, because then you know how did they have been invented and what was the reason to introduce them; what problems were they supposed to solve and how.

 

Their name actually says a lot already when you decipher it: It is a portmanteau of Greek words "logos" (ratio, relation between ideas) and "arithmos" = (number, rhythm, recurring pattern). They were called that way because their discoverer, John Napier, noticed that they are "indexes" which number the elements in the geometric progression. They are "numbers of the ratio", or how many times a certain ratio is to be applied to get to that term in a geometric progression. Today we would say that they are exponents of subsequent powers of a certain base. Look at the following geometric progression for the base 2:

 

2⁰ = 1

2¹ = 2

2² = 4

2³ = 8

2⁴ = 16

2⁵ = 32

2⁶ = 64

2⁷ = 128

2⁸ = 256

2⁹ = 512

2¹⁰ = 1024

2¹¹ = 2048

2¹² = 4096

2¹³ = 8192

2¹⁴ = 16384

2¹⁵ = 32768

2¹⁶ = 65536

 

Every time you get from one line to the line below it, you multiply the number at hand by 2 (or double it). Every time you go up a line, you divide by 2. So the 2 is the ratio between two subsequent lines, and since the ratio is constant, the elements in these lines follow a geometric progression (of continuous doubling in this case).

 

Notice that the numbers in geometric progression are subsequent powers of that ratio (2).

Notice also that the exponents of these powers (red) are subsequent natural numbers: they make arithmetic progression.

THOSE ARE THE LOGARITHMS! The "numbers of the ratios". They tell you how many times you need to multiply by that ratio (or the base) to get to that number. Or, in other words, to what power you need to raise that base to get the number in geometric progression.

 

So, for example, the number 256 from the geometric progression is a certain power of 2. Which one? Well, the logarithm will tell you. The logarithm is the exponent (you can use these terms interchangeably when you already know what they are) to which you need to raise the base to get that power. So, in our example, you need to raise the base 2 to the exponent of 8 to get the number 256 (which is the 8th power of 2). The (base-2) logarithm tells you which power of 2 the given number (256 in this case) is.

 

Logarithms are useful because they allow you to simplify your calculations.

They can reduce multiplication to mere addition, division to mere subtraction, exponentiation to mere multiplication, and taking roots to mere division. In other words, they allow you to step down a notch in the hierarchy of arithmetic operations.

 

To illustrate it, let's say you need to find the result of 64×512. You can cross-multiply it the old-school way (which is the slowest possible algorithm BTW ). But if you notice that they are both powers of 2, you can find their logarithms (indexes, exponents, ordinal numbers in the geometric progression) and just ADD these instead! Adding is much more easier than multiplying, isn't it? So the logarithm of 64 is 6, and the logarithm of 512 is 9 (with respect to the base of 2). So we have:

 

64×512 = 2⁶×2⁹ = 2⁶⁺⁹ = 2¹⁵ = 32768

You can ask though: How is it simpler if I need to calculate the powers?

Well, if that were the case, it really wouldn't be any more simpler.

But if you have all these powers of 2 TABULATED, as we did above for the geometric series of doubling, then you can simply look up these powers in your table (right column) to find their logarithms (the red indexes in the left column), then add them up, and look up the power of 2 for the resulting index to get the final answer. Try it for some other powers to convince yourself.

You can do the same for division: just subtract the exponents (logarithms).

 

This explains the first two formulae for logarithms:

 

log_b(p×q) = log_bp + log_bq

log_b(p/q) = log_bp - log_bq

As you know the logarithms are just exponents of powers, you can relate these formulae to the known "law of exponents" (which I can explain as simply if you wish), where you add exponents when multiplying the powers, and subtract exponents when dividing the powers.

 

From the second formula you can also figure out what is the logarithm of a reciprocal: just let p=1 and you get:

 

log_b(1/q) = log_b1 - log_bq = 0 - log_bq = -log_bq

since 1 is the zeroth power of any base. Therefore the logarithm of a reciprocal is just a negative logarithm. And this is understandable, since negative exponents are just shortcut notation for repeated division (similarly as positive exponents are shortcut notation for repeated multiplication).

 

There are standard tables of logarithms already made for us out there in math books. Or you can easily make such a table yourself in Microsoft Excel or OpenOffice Calc or any other spreadsheet software. Or you can use a calculator if your calculator has such a function. There are also methods for calculating logarithms by hand. (Of course there are! What did you expect? Calculators are not smarter than us, they're just dumb machines. They can only do what we taught them, just faster than us.)

 

The most useful observation of John Napier, though, is that logarithms to different bases are proportional. To illustrate this, let's write two geometric progressions of different ratios/bases side by side:

 

2⁰ = 1          = 4⁰

2¹ = 2

2² = 4          = 4¹

2³ = 8

2⁴ = 16        = 4²

2⁵ = 32

2⁶ = 64        = 4³

2⁷ = 128

2⁸ = 256      = 4⁴

2⁹ = 512

2¹⁰ = 1024   = 4⁵

2¹¹ = 2048

2¹² = 4096   = 4⁶

2¹³ = 8192

2¹⁴ = 16384 = 4⁷

2¹⁵ = 32768

2¹⁶ = 65536 = 4⁸

 

Can you see the pattern already? :grin2:

Every other power of 2 is also a power of 4. Therefore every other element of the second geometric progression is also an element of the first geometric progression. So the logarithms (indexes, exponents) of these elements would be twice as rare. For example the base-2 logarithm of 65536 is 16, because it is the 16th element of this geometric progression. But the base-4 logarithm of the same number is 8 (half of 16), because it is only the 8th element of the second geometric progression.

 

(BTW can you guess the exponents of the remaining powers of 4 in the right column? Hint: they will be fractions.)

 

Therefore, when you know the ratio between the exponents of the bases (1:2 in this case), you can easily convert between different bases! This is the rationale between the base-conversion formula for logarithms:

 

log_bp / log_bc = log_cp

(Note that the logarithm of the target base calculated in the original base is a constant, just some conversion factor between the bases.)

 

Now you know why is it the way it is

And I hope that the logarithms won't be mystery to you anymore

But if you had any follow-up questions, feel free to ask me.

Edited September 15, 2015 by SasQ

[Sakutama 30]

Hello! Any ladies still offering biology tutoring? My most sincere apologies the guys offering biology tutoring! It's just that I'm married, and from past experience having guy tutors led to WAY too many misunderstandings. So a lady tutor would help keep the peace. I hope you can understand. *sigh*

[SCS 7,443]

Shameless advertising ahead: I can help anyone with math up through and including multivariable calculus, as well as the basics of differential equations, and the basics of linear algebra/matrix theory/vector algebra. I can also help with HTML, basic CSS, and the fundamentals of Java programming. 

 

Anyone who sees this who desires help in those areas, feel free to send me a PM.

[Measure Theory 44]

Yo, anybody needing help with calculus or algebra (that includes the more basic side of linear algebra) I'm open to help! 

Edited September 25, 2015 by KasaiDragoness

[4april 374]

I want to learn Number Theory. It is part of the syllabus for the International Mathematical Olympiad.

 

Also, is there anyone else who is interested in participating in the IMO? If so, we can learn/ practice together.

[Twiggy 2,965]

Need help with history then I'm your guy

Edited May 9, 2021 by Twiggy

[ThatWeirdWhiteKid 9]

Spelling is my traed, I'm really good at it

[PastelHorses 69]

Explain one reason why a secondary storage device is needed in most computer systems?

[Ponies4Bronies 394]

I think it's something to do with storage and your computer being only to store a finite amount on it.

[Humphrey 49]

Explain one reason why a secondary storage device is needed in most computer systems?

I think it's a fail safe mechanism. If one storage is somehow broken, the data will still be preserved. 

[PastelHorses 69]

I think it's something to do with storage and your computer being only to store a finite amount on it.

 

I think it's a fail safe mechanism. If one storage is somehow broken, the data will still be preserved. 

 

Don't worry I got it. Thanks for the Help though!

[Codelyy 1,281]

I was wondering if someone would be able to help me with my assignment which is like homework but harder and it's for college XD.

 

Basically I'm doing work on information systems like functional areas in business such as marketing, finance and so on.

 

I've been given a task to describe the flow of information between these functional area's for two different scenarios. One is a mobile phone company wanting to release a new mobile phone but I've done that already. 

 

But the other which is the one I'm stuck on is the flow of information between functional areas for a new enrolment in a college and i was wondering if someone would be able to help?

 

(If you don't understand what i mean by the flow of information between functional areas. I basically mean what department/function in a business gets the enrolment form first and then what function do they sent it to next and why. So for example in a mobile phone company, I put finance goes to production to work how much it costs to make the phone and then production goes back to finance which then goes to advertising and so on.)

 

I will give someone a cookie if they help XD... I doubt anyone will know what I'm going on about since it's hard to understand at first i imagine... good luck!

[FlutterHigh 81]

So short story on my problem. My teacher is history class said for our project we can write about the history of anything since we are seniors and can make up are own minds. So the part off my brain that was clearly shut off said I'll do the history of a brony since i have been one for four years.

 

I have a six page outline/rough draft assigned today due Friday and am having trouble compiling enough info for a six page essay

 

Due to the rules of no plagiarizing if anyone can help find some info with works sited in chicago style it would be much appreciated thx for taking the time to read and reply.

 

I can use film references,written,web sources,and Interviews

 

If you want send me a pm to let me know if i can send you a question to answer for the interview section.

 

[Flying_Endeavor 73]

Umm.. I am a bit lost here, anything specific that you might need.. O-o

[Ponies4Bronies 394]

You will be struggling to find stuff for six pages for a fandom that has been around for five years. Try writing about China, they have a ridiculously long history, from early times, to dynasties, to foreign imperialism, to World War II, to Communist China and then modern China and try for a page on each for your six pages. But if you really want to write about Pony then you are welcome to pm me for an interview.

Edited December 16, 2015 by Rainbow Dashe

[Flying_Endeavor 73]

Yeah, for sure you have other alternatives. Try WW2 as a whole. That would surely be filled with content on its own.  

[Fhaolan 4,468]

@@FlutterHigh, your request for history project help has been merged with the more general 'homework help' topic.