Exponent Definition and 220 Threads

I've seen the use of a negative exponent in the books and articles I've been reading lately, and I was wondering exactly what it meant. Such as 300 cm-1, where cm has a -1 as the exponent. (Dont know how to type that out.) What does it mean?

Hello Physics Forums, I read around and saw a few examples for Fermat's last theorem for exponents 1 and 2, but I was wondering if this can be proven for exponent 3. That is: Proof that IF x^3+y^3=z^3, where x,y, and z are rational integers, then x, y, or z is 0. Can this be done?

Most quantum textbooks will tell you that converting between the Schrödinger and Heisenberg pictures involves something like the following: |\Psi(t)\rangle = e^{i\hat{H}(t-t_0)}|\Psi(t_0)\rangle This does make sense to me conceptually: we define eigenstates of the Hamiltonian |E\rangle, where...

Homework Statement Use your knowledge of exponents to solve \frac{1}{2^x} > \frac{1}{x^2} Homework Equations The Attempt at a Solution x^2 > 2^x Then I am stuck. I know they intersect at x = 2.

I was trying to figure out the relation between the equation of a discharging capacitor and the Natural Inverse Exponent function v(t) = Vo*e^(-t/rc) A*e(-Ct)+B I get that A represents the voltage and the C is the inverse of the time constant but i can't figure out what the B stands for

Homework Statement f(x) = 10(sin(x))^x ----> find f '(1) The Attempt at a Solution I have tried several different approaches, but still get stuck with a wrong answer every time f(x) = 10(sin(x))^x let f(x) = y so y=10(sin(x))^x then ln y = ln10(sin(x))^x...

Homework Statement Determine the nature of the singularities of the following function and evaluate the residues. \frac{z^{-k}}{z+1} for 0 < k < 1 Homework Equations Residue theorem, Laurent expansions, etc. The Attempt at a Solution Ok this is a weird one since we've...

Homework Statement I would like to solve the following equation for the variable "n" The variable c represents any integer constant. (n/2)^n = c The goal is to get this in some form of n = ? Homework Equations The logarithm properties. The Attempt at a Solution I've tried...

Homework Statement Solve for x (1/10)^(x - 1) < (1/10)2. My Dilemma The problem is that using one method will yield one answer, but using another method will yield another. Why is that? Please help. My issue is not regarding the right answer (the right answer is x > 2). It's regarding the...

I have a function f(x) such that f(x) = x^{\frac{a}{b}} where {\frac{a}{b}} is noninteger. Is there an equation to solve this? A series expansion or something? I've looked around and couldn't find anything.

Homework Statement 2x-2 - 2 = 5 - x Find x. Homework Equations log(a)x = y The Attempt at a Solution I've thought about this a lot and the best I could come up with was getting to ... x = log(2)(12 - 4x) The problem is that I seem to be going in circles and I can't drop x...

I am trying to do a very simple problem on MATLAB, but I do not know much about MATLAB so this is challenging. Here is the code: y=0:50:300; D=0.210; % D is the mean sediment diameter w=14*D^(1.1); % w is the particle fall speed A=0.067*w^(0.44); % A is the sediment...

Homework Statement 3^2x - 12 * (3^x) + 3^3 = 0 solve for x The Attempt at a Solution I did this question just by factoring it into a more convenient form 3^x ( 3^x - 12) = -27 which tells me x>2 (in oder to make the bracket term, and hence the product, negative), and that x is a...

Ok I mucked up the question given VT^{\frac{f}{2} = constant T = PV Need help simpi ------- I get V (PV)^{\frac{f}{2}} which is the same as V P^{\frac{f}{2}}V^{\frac{f}{2}} which is the same as P^{\frac{f}{2}} V^{\frac{2+f}{2}} Now how do i simplify it from here? answer is...

Homework Statement Find the critical numbers of the function: F(x) = x^(4/5) (x - 4)^(2) Homework Equations None. The Attempt at a Solution I differentiated and got to (1 / 5th root of x) (x - 4)(2x + 4/5(x-4)) but I don't know how I can simplify the expression to be able...

Just out of curiosity, I was wondering how to solve for x in an expression of the form ax = xb It kinda tripped me out at first.

i need to calculate e^{-0.5} why the solution develops e^{-x} and puts 0.5 and not e^{+x} and putting -0.5 ?

how this thing works ? integration of e to the power of (-x) from 0 to infinity sorry , not good in using the symbols ..^.^ ~

I'm trying to calculate maximum power. Once I computed power as a function of time I took its derivative and set it equal to zero. Now it need to solve for time and I can't seem to get it done. What I have is... -1000e^{-500t}-2000e^{-1000t}=0 My first inclination is to use ln, but ln(0)...

So, I took an exam on conversion of units in chemistry and I put a negative exponent on the bottom: 100s* 1nanoseconds/10^-9s = 10^11 ns, Is this wrong? If it's possible in math, why not in chemistry? My professor marked all my answers wrong due to this. Is there any way to argue my...

\frac{2i}{2+i} i don know how to separate the complex and imaginary part of this fracture?

1. The problem statement, all variables a sample polonium-218 decays at A(t)=100(.5)^t/3.1 determine how many minutes it will take to decay to 30% 2. Homework Equations log(a)/log(b) 3. The Attempt at a Solution .3=100(.5)^t/3.1 .3/100=.5^t/3.1

Homework Statement Speed of an ocean wave depends on the wavelength \lambda in meters and gravitational field. (see equation below). Find values of P and Q. K is a constant and has no dimensions Homework Equations V = K\lambdaPgQ The Attempt at a Solution V=velocity, which is...

I'm just wondering because I found this crazy picture somewhere on the net. http://photos-h.ak.fbcdn.net/hphotos-ak-snc3/hs071.snc3/13845_1261921983558_1094945438_30798960_833983_n.jpg

when is it justified to do something like this \lim_{n\to\infty} e^{lnx^{1/n}} = e^{\displaystyle\lim_{n\to\infty}lnx^{1/n}} or something like this \lim_{n\to\infty} 2^{f(n)} = 2^{\displaystyle\lim_{n\to\infty}f(n)}} ? I am assuming that I can do something like this in both cases...

Can you please help me sort out my terminology? Are 'power', 'index' and 'exponent' exact synonyms, even thogh they tend to be used in different contexts? If a^x gives 'exponential growth' is the growth described by x^a also properly called 'exponential'? If not, what is it called...

I have just begun studying differentiaition and I was getting confused with how to differentiate a function of x in which x is in the base and is in the exponent as well (for example, x^2x) with respect to a=hte cahnge in 'x'. I remember my teacher telling me something about applying log...

I am calculating the likelihood of a hierarchical model and am having trouble distributing the product sign. Here are the two expressions that I'm interested in: Product from j=1 to j_k of: (t_jk)^(sum(Z_ijk) + a_k - 1) and Product from k=1 to K of: (b_k)^(j_k*a_k). The tricky...

I am calculating the likelihood of a hierarchical model and am having trouble distributing the product sign. Here are the two expressions that I'm interested in: Product from j=1 to j_k of: (t_jk)^(sum(Z_ijk) + a_k - 1) and Product from k=1 to K of: (b_k)^(j_k*a_k). The tricky...

Negative Lipschitz (Hölder) exponent: Intuition! Hi everybody! Sorry for double posting... :( I have some problem with Hölder (Lipschitz) exponent! From what I know Lipschitz refer to integer values whereas Hölder to non integer ones. The usual definition roughly states that: A...

Homework Statement lim as x approaches 0 of (x + 1)ln x Homework Equations The Attempt at a Solution I tried using ln y = (ln x)[ln (x + 1)] then: ln (x + 1) ---------- 1 --- ln x to make it eligible for L'Hopital's Rule. Then differentiating the numerator and the denominator, I got: 1 --- x...

hello, I am trying to follow the arguments in Peskin pages 96-97 where the exponentiation of disconnected diagrams are performed. I think the 'proof' is too 'not detailed' and was wondering if there exists a better explanation elsewhere? My biggest question is the sentence on page 97 "The sum...

Homework Statement find n. Homework Equations 2^2^n = 36trillion The Attempt at a Solution I have worked this out and found n to be equal to 3.67 can someone confirm that i have the right solution? I took the log on both sides and worked it out.

Hi, I'm trying to solve the following: f(x) = \int^\infty_{-\infty}ce^{yx-y^2/2} dy where c is a constant My only idea thus far was that since it is an even function, the expression can be simplified to: = 2c\int^\infty_0 e^{y(x-{1/2}y)} dy but I'm stuck here. Anyone know how to do...

I can't remember how to solve an equation of the following form: ln(a^x) = ln(b^x) I want to solve this for x where a and b are both real numbers. I know I can manipulate the logarithm to write: xln(a) = xln(b) But this just seems to cancel out the x's. If you can show me how to...

Homework Statement i need to solve for b in f(x)=a*xb i know f(1.5)=10 and f(1.7)=14 it's been forever since i did calc like this and i am blank on what to do. i can't remember if or how i can set them equal to each other to solve for b. i know i have 2 eqns and 2 unknowns. do i set...

Homework Statement All I am trying to do is the basic mathematical induction routine: n=1, n=k, n=k+1 and how n=k proves n=k+1. The problem I am having is with the algebra. 4+16+64+...+4^{n}=\frac{4}{3}(4^{n}-1) 2. Homework Equations and Attempts For n=1 4=4 That's OK For n=k...

Homework Statement (3xy^3)(4x^-3y^-2) Homework Equations ? The Attempt at a Solution = 12y ----- x^2

hello.i have a weird problem. (-8) ^ (2/6) = ? my first instinct was to simplify the exponent, which yields (-8) ^ (1/3) = -2. this is the answer the calculator gives as well. but someone pointed out if you don't simplify that exponent, you have the sixth root of (-8^2), which would...

Hello everyone! The following question stumped me and I thought you may be able to help. If x^y = 2 and x^t = 16 what does x^(y-t) equal? I don't know where to start so any help would be appreciated. Thanks, Ben

Homework Statement Calculate \int_{0}^{4}\sqrt{x} e^{\sqrt{x}) The Attempt at a Solution At first I tried substitution, but this didn't bring me anywhere since the integral is not of the form \int f(g(x))g'(x) My attempt at integration by parts also leads to an endless loop...

Homework Statement 0^{\sqrt{0}}=\sqrt{0^{0}} Is this expression true?

Let A be a bounded operator in complex Hilbert space. Prove that \sigma(Exp(A))=Exp(\sigma(A)). It is known, that \sigma(P(A))=P(\sigma(A)), where P is a polynomial. In addition, if an operator A has a bounded inverse, then for any operator B such that ||B||<1/||A^{-1}|| their sum A+B...

Hi, I don know how to go about expanding things such as 3x\sqrt{3x-1} apparently that equals 12x^{2} - 4x i know that 3x\sqrt{3x-1} can be written as 3x(3x-1)^{\frac{1}{2}} but i don't know what to do. I can't remeber. Thanks :)

[SOLVED] Summation Notation - Variable in the exponent Homework Statement This is an example formula. How do I solve a summation if something is in the form of Sum(c^i), where c is some constant?

Can someone please clarify: If i wish to write2^(√2) as an exponent am I correct in thinking this will be written as: exp√2(ln2) ? Thanks

Homework Statement 6^1+6^-1 / 6^1-6^-1 (Question is to evaluate that, but I am going to venture to guess that we are supposed to somehow simplify the question a lot further. We just finished learning all the exponent laws) Explain how you can tell which is bigger without evaluating...

How do you derive the value of an exponent? I have to derive the value of the exponent n in the following equation: x = At^n , where A = constant

Homework Statement Suppose we lived in a matter-dominated, critical-density universe. The matter density rho of such a universe changes with time t as a power of t. Derive the value of the exponent n in the following equation: Homework Equations rho = At^n where A = constant

Homework Statement Find the local max and min f(x)=xe^x Homework Equations first find the derivative of xe^x and then set it to 0 The Attempt at a Solution I understand how to approach the problem but I don't know how to break apart the original equation since there is an...