unusual algebra question

Jeff12341234

I need a list to reference when solving for a variable in any algebraic problem. For example, solve for y: 1=e^2y. You'd go down the list looking for the function e^nm and right next to that, you'd see the function needed to undo that function at least partially. Then, with whatever you're left with after applying that, you'd go down the list again repeating the same steps until Y is alone. I can't possibly be the first person to think of using such a list. Therefore, it must already exist somewhere. I can't find it on google though.

micromass

Such a list doesn't exist, it would be too large.

Jeff12341234

i don't see how it would be that large.. you've got basic math operations, log and ln, e^x, the trig functions, the two calculus functions d/dx and integration, exponents, exponents to exponents, etc.. I don't see how there are that many.

micromass

There are infinitely many bijections, so the list would be infinite.

Of course, if you are asking about commonly used functions, then the situation changes. I'm sure such lists exists. But they are not complete or exhaustive.

Jeff12341234

sure. a list of commonly used functions that covers everything from algebra to diff eq would be nice. I don't know why it's such a hard thing to find. It would be very useful..

micromass

http://www.amazon.com/Handbook-Mathe.../dp/0521140633

Jeff12341234

I just got done downloading and briefly looking through that book. Nowhere is there a list of what I want. It's 99.5% not the answer to the question.

micromass

I know. But it's the best I can come up with. It would surprise me if you would find what you're looking for.

HallsofIvy

Did you honestly expect that someone would have made a "list" that contained exactly what you wanted? That would be like posting a list giving the sum of any two numbers! Sooner or later, you will have to augment "lists" with a little basic knowledge. There are "lists" giving the sums of one or two digit integers. After that you have to know how to use those to get sums of larger integers and decimal numbers.

Just as for a problem like this, once you know the logarithm function, you apply that: if [itex]2= e^{2^y}[/itex] then, taking the logrithm of both sides [itex]ln(2)= 2^y[/itex] and, since you still have an exponential, do it again: ln(ln(2))= y ln(2).
(I changed from your "1= " because that is too easy. If [itex]e^{2^y}= 1[/itex] then [itex]2^y= 0[/itex] which impossible.)

Jeff12341234

There's nothing weird about it. For a student in college algebra - DiffEq, there aren't infinite items that would need to be on the list. Only about 100 or so I would think.

Another example is you see y² = 25. You look down the list to find out what the opposite function of squaring something would be. The list says square-rooting will undo it so you square root both sides and get y=±5. What's so strange about having a list like that? I don't want to have to make one just to prove how feasible it is because someone has likely already done it.

Stephen Tashi

You are asking for a list of "inverse functions". What's strange about it is that people who want to go into technical fields develop enough competence in mathematics to reason out the answers to such questions without needing a list.

There are certainly some problems where people with average competence in mathematics find lists useful - such as tables of integrals. Nowadays, computer programs are often substituted for such tables. The kind of list you want wouldn't be useful to mathematians. I can sympathize with the fact that struggling students might find such a list useful in doing homework, but the use of such lists might prevent them from learning the ideas involved.

AlephZero

There is a computerized "list" it's called http://www.wolfram.com/mathematica/

You might have a problem taking it into your exams, though.

Jeff12341234

If you don't know the answer to the specific question, then please don't spam with obvious bs responses. I tutor college algebra students. A list as I described would be a great teaching/reference tool for them to use until they got them memorized.

micromass

So give them a problem and let them look on a list to see which steps they have to take? I'm sorry, but that is a horrible way to teach mathematics.

But anyway, the list you are talking about doesn't exist. Thread locked.