Exponents Definition and 268 Threads

Homework Statement 7. Between 1950 and 1989, the world’s population grew by 1.85%/a. (a) Determine the doubling time for this example. (b) If the population in 1950 was 2.5 billion, what was it in 1989? Homework Equations dt = 72%/growth rate The Attempt at a Solution a. dt =...

Hey guys I need help how to solve this equation... Express your answer to the equation in the form alnb 9e^4x-e^2x=0 This is as far as I got 9e^4x=e^2x ln(9e^4x)=ln(e^2x) the answer given in the markscheme is x=1/2ln1/9, x=-1/2ln9, x=ln1/3, a=-1/2 and b=9, x=-ln3 (accept a=-1 and...

I am playing around with the set {e^(2ki)|k=intiger}. all of these numbers when raised to the pi power give one (at least as one possible value). In other words, they can all be thought of as values of 1^(1/pi). There are a countable infinity of them, and I believe that these numbers are...

I'm reviewing for a test. One of my questions on the review (and incidentally a question I've had in my own mind for a long time) is how do you evaluate an ARBITRARY rational exponent with pencil and paper and no calculator? The specific problem i was givens is "Solve without a calculator...

what are the restrictions (if any) on y=1/x^(-2)? is it equal to just x^2 so no restrictions or what it is have hole at x=0? or do you change too all positive exponents before looking at restrictions? what exactly are the exponents rules that govern this stuff so confused

The question is x2/3 - x1/3 - 2 = 0 So the first thing I did was: x2/3 - x1/3 = 2 Then, I put both sides to the power of three, so I got: x2 - x1 = 8 From there I factorized: x (x - 1) =8 And got the answers: x = 8 or x = 9, the book however, says the correct answers are -1 and 8. Any...

HI guys, I just started university and I have no idea what is going on in my lectures. My lecturer doesn't explain anything well and he is also the bloke who takes my tutorials. Lose - lose situation! Anyways I am trying to learn this myself, but I am stumped on this question: Homework...

Why should the exponents of polynomials just be whole numbers ?

It is clear that 10^2 can be simplified to 10*10=100. But what about say, 10^0.5? I have been thinking about this for days and can't figure out how it simplifies. 10^1 is 10, 10^0 is 1, so 10^0.5 should be under 1, but it is 3.16, so I don't get it. Same with 10^-1 is 0.1. How exactly are...

Homework Statement differentiate y = t^{5-e} Homework Equations Power rule The Attempt at a Solution u = (5 - e) (u)t^{u - 1} = (5 - e)t^{4-e} Is this a correct usage? I'm not sure if there are any equations regarding this, but since e is a constant this should be correct right?

Hello, I did the integral of a Fourier Transform which resulted in this: A(je^(-jwe^(To+t/2) - je^-jw(T0-t/2))/(1/w) Where A is the amplitude, j the imaginary number, and w is omega or 2*pi*f. My question is, how can this be further simplifier. I am forgetting how to simplify...

We have: z = (2^(mn) - 1)/[(2^m - 1)(2^n - 1)], where (2^m - 1) and (2^n - 1) are prime numbers. Prove that (2^m - 1) and (2^n - 1) are not the only prime factors of z. I tried to solve it writing z = (2^m - 1)^a * (2^n - 1)^b and proving that it is not correct. But I don't know how. I also...

1. Homework Statement Find the derivative. 2. Homework Equations h(t)= t^(pi^3)+(pi^3)^t+(pi)t^33. The Attempt at a Solution - i know that pi is a constant (number) so when finding it's derivative, it will be something like, (2nd part= (pi^3)^t ) : ln pi (pi^3)^t * 3t - 3rd part = (pi)t^3 ...

Homework Statement Calculate (5^7)-(7^7)+(9^7)-(11^7) in Mod24 Homework Equations The Attempt at a Solution I added all the bases and got -4 (which I changed to 4), then I took 4^7 and ended up with 16,384. I divided 16,384 by 24 as many times as I could, which gave me an end...

Homework Statement Calculate 2 + 3^2 + 5^3 + 3^2*5^3 in Z15 (That last group of numbers means 3 to the 2*5 power then take this answer to the third power, It just did not paste like that) Homework Equations The Attempt at a Solution 2+9+5+3<--the 3 is a random guess, because...

Homework Statement If f(x) = 2sin(x) + (4x)^x find ---> f ' (3) Homework Equations d/dx (e^u) = e^u du/dx The Attempt at a Solution Here is my attempt: f(x) = 2sin(x) + e^(ln(4x)^x) = 2sin(x) + e^(xln4x) = d/dx (2sin(x)) + d/dx (e^(xln4x)) = 2cos(x)...

Answering the above question is not really hard, but the question is how to change 32^24 to 2^120? Whats the method for that? Is there a formula I can use?

Homework Statement lim h->0 [(11+h)^-1 - 11^-1]/h Homework Equations The Attempt at a Solution I made the numerator into two fractions with the denominator h. After combining the fractions in the numerator I was left with 121 when I put in 0 for h.

Homework Statement Attached is the problem, I don't like the math editor used on this site, so its a pdf. The only real problem I have is how to is how do you square a problem like square root of x over 2x?

Homework Statement 4 1/(x+1) · 8 1/(x+2) = 9log3 2 Homework Equations n/a - same as 1 The Attempt at a Solution To get rid of the exponents and be able to solve for x, I first took the logarithm with base 4 of all terms: log44 1/(x+1) · log48 1/(x+2) = log49 log3 2 This equals: 1/(x+1)...

Homework Statement So I'm going over the simple yearly interest formula A=P(1+r)^t, where 't' is in years, 'P' is in dollars and is the size of the initial investment, 'A' is in dollars and is the total interest earned in a given period of years, and 'r' is the rate at which the investment...

I've been toying around with stuff I probably shouldn't be. :biggrin: I've been sketching a graph of y=x^n where n is a rational number (as opposed to an integer). Of course, when I get into the fractional exponents, the negative portion of the curve ends up being imaginary (eg. x=-2,n=2.5...

How can we find irrational exponents of a real or imaginary number?? say 2 raise to the power pi

I just started reading my physics book again, and one of the very first things it talks about is proportionality. I understand the concept that two things are proportional if one gets multiplied by a certain factor and the other one has to be multiplied by the same factor. For instance, if...

Homework Statement my integrating factor for the DE ty' + (t+1)y = t is mu(x) = e^integ (1+(1/t)) = e^(t + ln|t| + c) so does this simplify to this...or not? = e^t + t + c so that DE becomes: ((e^t) + t))y = (e^t) + t) and then after integrating... ((e^t) + t))y = e^t +...

Homework Statement 9 - 9y-2 ____________ y-1 - y0 this whole thing is then raised to 2 (I can't seem to format it that way:( ) Homework Equations none The Attempt at a Solution I'm hoping someone would guide me through this :(

Homework Statement (35.709 + 5.789)(10^4 + 10^4) =41.498 * 10^4 Homework Equations this is an an example given in my TEAS (standardized skills test) work book/study guide...is it accurate? i don't know why (10^4 + 10^4) = 10^4 after the simplification The Attempt at a Solution

How do you prove the following? 7^{\sqrt{5}} > 5^{\sqrt{7}} Without calculators or working out {\sqrt{5}}, {\sqrt{7}}, of course.

When the direct product is in the exponent of some variable, how is it defined?

So I just got back from my math class, we were going over exponents. Right before we left he gave us a problem and we turned it in, I was just wondering if I got it right. Simplify: (54-3y)3 * (5y-2)2 I got: 512-9y3 * 5y2-4 5-9y3+y2+8 I applied the powers to the parenthesis, then...

Homework Statement I barely even know where to begin with this proof: Show that the product of two of the numbers 651000 - 82001 + 3177, 791212 - 92399 + 22001 and 244493 - 58192 + 71777 is nonnegative. I also have to state if it is constructive or nonconstructive, and I'm not supposed to...

Homework Statement 4a^4b^3 -a^3 ---------- x ------- a^5b^6 -(b^2) Homework Equations The Attempt at a Solution (4a^4b^3)(1a^3) = 4-a^7b^-3 --------------- a^5-b^4 = $-a^2b^-1 WHERE DID I GO WRONG!

Homework Statement When there are exponents in a radicand as shown below, do i just divide them out? Homework Equations ∛(x^6 y^4 ) The Attempt at a Solution x^2 y^4 ?

Nevermind Solved it.

I know that if you have x-2, that's the same thing as saying 1/x2. But I'm just wondering what is the mathematical reasoning for why that's true? Thanks!

Modular method in solving numbers raised to high exponents Arrange the ff from greatest to least: 2^{110}, 3^{75}, 5^{49} How could I use a modular method to be able to answer that one? I really need it. Hope you could help me.

Homework Statement This is just a general question, not a "problem" Homework Equations Z = sum(e^Ej/kT) The Attempt at a Solution I'm working on a problem in which I'm asked to find the probabilities of an electron in a hydrogen atom being at one of three energies. The...

Where are they found?

Find B when given: Y = log2B and 2y+4 + 4y+3 = 224 I could use some help figuring out the process to this. Thanks

Homework Statement 1/ 2^10 + 1/ 2^11 + 1/ 2^12 + 1 / 2^12 = ? Homework Equations The Attempt at a Solution i am very confused with this problem as i thought that i would convert the 1/2^X numbers to 2^-X and then add the numbers together. The answer would be 1/2^45. and i know...

Fractions, Exponents, and x :( I simply just don't get fractions and exponents i was given this problem: [6x^(4/5)-3x(2/3)]/3x^(1/3) i haven't gotten anywhere and I'm stuck help thanks in advance

Ok, I have a number to the power of another, say 2^3 which of course is 8. Question is if you have 2^n = 8 how do you calculate n?, this is obviously simple for the example but say if I needed to calculate n in 2^n = 1000 how do I do this either on paper or using a calculator, I've searched the...

Homework Statement Factor 3x (4x-1)^-2 - 6x^2 (4x-1)^-1 Homework Equations The Attempt at a Solution

In an experiment I am performing, I observed the following: Result is directly proportional to A Result is inversely proportional to B So, I assume two constants, alpha and beta such that: Result = (A^alpha)/(B^beta) Now, if I know I want to solve for alpha and beta but is this the...

Hi everybody! I'm looking for the critical exponent ν (i.e. the one of the correlation length) of the Heisenberg (i.e. equal coupling in all directions) antiferromagnetic spin-1/2 model in 1D... Furthermore, do you know to which universality class it belongs? Is it true that it's the...

Is the power rule in calculus true for any complex exponents? i.e. does d/dz z^c = cz^(c-1) true for any c, even when c is something like i or 3i-2?

Hello reader So I'm trying to teach mysel calculus with Thompson's Calculus made easy. I'm still in the very early stages and I got stuck with negative exponents. I'd basically like an explanation fof what's going on here. http://www.flickr.com/photos/26906498@N03/3705112800/ I've...

Homework Statement 2x^(-1/3)-9x^(-1/6)= -10 Homework Equations ? The Attempt at a Solution I have tried to factor out x^(-1/6) x^(-1/6) (2x-9)= -10 I'm not sure that's even right I have also converted to fractions 1/2x^(1/3)-1/9x^(1/6)= -10 I'm not sure which route to go or if...

Homework Statement Prove: $\left(ab^{-1}\right)\left(cd^{-1}\right)^{-1}=\left(ad\right)\left(cb\right)^{-1}$. I know how to distribute exponents to get both sides to look identical... Homework Equations ...but a step in the solution requires distributing exponents. But how do...

Homework Statement (4x-1)^{1/2}-1/3(4x-1)^{3/2}Homework Equations The Attempt at a Solution I think the GCF is (4x-1)^{1/2}. So, I get (4x-1)^{1/2}(1+(-1/3(4x-1))) = (4x-1)^{1/2}(-4/3x+4/3) = -4/3(4x-1)^{1/2}(x-1) However, the answer in the book is 4/3(4x-1)^{1/2}(x-1). I've done it several...