Log Definition and 618 Threads

Hello, Consider x \in (0,1) , that is x between 0 and 1. Can someone explain why the following is true: \frac{x-1}{x+1} = \tanh \left( \ln \left( \frac{x}{2} \right) \right)

What Product Log Means?? Hi, I have the following equation: B = (k*a*Exp[-t*(B/N)*T/beta] - N)/(a*Exp[-t*(B/N)*T/beta]) Using Mathematica, I tried to solve it for B. Mathematica returned the following solution: B = k-(N*beta*ProductLog[(E^((k*t*T)/(N*beta))*t*T)/(a*beta)])/(t*T)...

Homework Statement Hi guys, I'm stuck on this question in exam revision: I need to estimate the area under the following curves (I don't have the equations of the curves) http://img819.imageshack.us/img819/3249/question.jpg The curves are magnitude diagrams in the log-log scale...

Hello, if I have a function f:\mathbb{R}\rightarrow \mathbb{C}, what are the conditions on f for which the derivative of the Logarithm exist? \frac{d}{dx}\mathrm{Log} (f(x)) exists? Note that here I defined: Log(z)=\log |z| + Arg(z), where -\pi< Arg(z) \leq \pi

Homework Statement integral of secxtanx/secx -1 Homework Equations sec u du = ln |sec u +t an u | + c The Attempt at a Solution sec u +tan u | + c

Homework Statement integral of x/square root of 9- x^2 Homework Equations 1/x dx= ln |x| + c The Attempt at a Solution 3 ln|x| + c

Hi, everyone: I am confused about the def. of winding number of a loop on S^1 ( on elements of Pi_1(S^1,1) ). The winding number is defined by w(f):= [log(f)1)-log(f)0)]/i2Pi One of the problems is that log cannot be defined continuously on S^1, since complex logs can only be...

Homework Statement using the following definition: ln x = \int dx/x, give best possible upper and lower estimates of ln n, n a positive integer. then, use this result to show that the limit of the function as n approaches infinity is infinity. Homework Equations -- The Attempt...

Hi, here's some information after fitting measurements to a lognormal distribution. What exactely does it mean that the log likelyhood is -67.175?? As of my understanding the log likelihood, is the natural logaritm of the likelihood function, which is the probability that these measurements...

Homework Statement I've been going through a book called "Short Calculus: The Original Edition of A First Course in Calculus," by Serge Lang. It says, " The derivative of a^x is a^x (log a)." But everything else I look at says the derivative of a^x is a^x (ln a). Since ln a and log a are...

Homework Statement log39 + log41/64 + log51 Homework Equations none The Attempt at a Solution I tried answering it by... (3x=9) + (4x=1/64) + (5x=1) because of this, I got 5. Is that correct?

Write the following log equations as exponential equations and vice-versa. 1.) ln 0.5 = - 0.6931 Differentiate with respect to x. 2.) y = e^x(sin x + cos x)

Write the following log equations as exponential equations and vice-versa. 1.) ln 0.5 = - 0.6931 Differentiate with respect to x. 2.) y = e^x(sin x + cos x)

Homework Statement Im trying to find the uncertainty for a log function. I have that f = 20log(V_in/V_out) and i want to know (delta)f Homework Equations f = 20log(V_in/V_out) The Attempt at a Solution I was going to do it the calculus way: f = 20log(V_in) -20log(V_out)...

Homework Statement Find the limit as n--> infinity of (1-2/n)^n Homework Equations We know (1+1/x)^x --> e as n--> infinity The Attempt at a Solution I worked it out as e^(-2) using log but I can't get it out using the fundamental limit above. I know it's the square of (1-1/x)^x...

Hello, I am fairly new here, so thank you in advance for your help. This is not a homework problem, just one of curiosity based on my limited knowledge of asymptotic expansions. I'm curious about how the function ln(x) or ln(1+x) behaves for large values of x. Plotting in Matlab, I see a linear...

Hi I want to know is it possible to differentiate exp and log functions where bases are functions not constants?How? Thanks

I posted this in the mathematical/computation software forum but maybe there's an algebraic trick I don't know to help me solve this. I need to compute an integral of: \sqrt{\text{E1}^2-m^2} Log\left( \frac{m^2-m_B E1-m_B\sqrt{E1^2-m^2}}{m^2-m_B E1+m_B \sqrt{E1^2-m^2}}\right) over the...

I have an integration to perform \sqrt{\text{E1}^2-m^2} Log\left( \frac{m^2-m_B E1-m_B\sqrt{E1^2-m^2}}{m^2-m_B E1+m_B \sqrt{E1^2-m^2}}\right) Sqrt[E1^2 - m^2] log((m^2 - mB (Sqrt[E1^2 - m^2] + E1))/( mB (Sqrt[E1^2 - m^2] - E1) + m^2)) over the region {E1,m,mB/2} E1 is the variable. m is...

Homework Statement Trying to solve for K: ln(1-4k)=-6k Homework Equations The Attempt at a Solution I know that need to take the e of both side, to get 1-4k=e^-6k, but I cannot remember any properties of e to allow me to remove the k from the exponent. Any tips is appreciated.

Homework Statement If log_{}2n(1944) = log_{}n(486\sqrt{}2) then evaluate n^6 P.S the 2n and n are subscripts. Homework Equations log base b(a) = c is the same as a^c = b The Attempt at a Solution I tried converting log base 2n to log base n but I ended up nowhere.

I am trying to solved a differential equation of Bessel type, X^2 Y('')+XY(')+(X^2-n^2)Y+YlogX=0, where Y(')=d/dx. Please help me that how to deal with such equation.

Homework Statement I want to find the limit as n approaches infinity of (n^n)*(x^(n^2)), and Homework Equations My teacher told us to look at the log. 0<x<1. Also, since the log of this goes to -infinity, then the original limit in question goes to 0. (1) why is looking at log valid...

I'm new here. You already knew that. Thank you, you, for clicking on my thread in any case. So, I've got these two log problems. My math teacher gave them out as a challenge. The class is relatively new to logs, and I'm having trouble working with these longer questions (longer than "simplify...

Here is an equation: x^3 + 1 = 3^x We have no problem of taking ln of both sides, right? But if we write the equation as x^3 - 3^x + 1 = 0 Now let's take ln of both sides ln ( x^3 - 3^x + 1 ) = ln (0) But ln (0) is undefined. My question is: After just taking 3x to the...

Homework Statement \int^{4}_{2} \frac{dx}{x\left(lnx\right)^{2}} Homework Equations Let u=lnx du=\frac{1}{x}dx x=2 \rightarrow u=ln2 x=4 \rightarrow u=ln4 The Attempt at a Solution so with the u substitution we have: \int^{ln4}_{ln2} \frac{1}{u^{2}}du which goes to...

Homework Statement Find x: log 3 (x^2 -5x+6) - log 2 (2-x) = 2 Homework Equations The Attempt at a Solution I tried and got: (3-x).[(2-x)^1-log 2 (3)] = 9 but I don't know how to get x here ...

Q: Logx = 1 + 6/logx my attempt so far: Log x^2 = 7 where do i go from here?

Homework Statement Only the equation: 2(3^x) = 7(5^x) Homework Equations N/A The Attempt at a Solution Okay. I've been fine learning the loglaws, until I hit this question. If they were the same base (or at least near the same, ex: 2 & 8) then I could simply change them into...

Homework Statement Solve dy/dx = exp(x-y) given that y = ln 2 at x = 0Homework Equations None.The Attempt at a Solution Firstly let's get the equation into a form so we can re-arrange the x's and y's, and then re-arrange. dy/dx = exp(x)/exp(y) exp(y)*dy = exp(x)*dx Integrate: exp(y) =...

Homework Statement 0.5log(2x-1)+log\sqrt{x-9}=1 Homework Equations N/A The Attempt at a Solution I have no idea how to approach this.

Homework Statement 5^(log510-1) Homework Equations n/a The Attempt at a Solution I have no idea how to approach this.

Homework Statement Merry Xmas~ I hope there's still someone online during the holiday season. I'm trying to solve a set of static laser rate equations but with log in the expression. I think, there's no analytic solution but I don't really know how solve the problem numerically with Matlab...

Homework Statement Solve: log(sub6)x+log(sub6)(x-5) = 2 Homework Equations na? The Attempt at a Solution i multiplied the second log out and got: log(sub6)x+log(sub6)x-log(sub6)5 = 2 then i put the x's on one side and the numbers on the other. 2(log(sub6)x) = 2+log(sub6)5...

Homework Statement y = \log_{2}(x^2 + 1) Homework Equations I think the pattern is: \frac{d}{dx}[\log_{b}(x)] = \frac{1}{x ln(b)}The Attempt at a Solution y\prime = \frac{2x}{(x^2+1)ln(2)} I did this by applying the pattern (that may or may not be correct) and then chain ruling the...

Hello! If I have the gaussian function, but x is a loarithmic scale. Can I infer that, if x was plotted using a regualr scale, that the function would be 'fairly' linear? At least initially? As the rate of change gradually increases befor slowing down again. I think this is reasonable... I...

Solve the equation log4x=1+log22x, x>0

Homework Statement Solve ln(sinh-1(x)) = 1 (Just give the formula for x, no calculator is necessary) sinh-1(x) = asinh Homework Equations The Attempt at a Solution When I did this, I knew sinh-1(x) = ln(x + sqrt.(x^2 +1), but the equation would look like ln(ln(x +...

Homework Statement This is my first time ever posting anything on here...but we just started working with ln? I know that it's the base e? or something like that... but the problem is this... 1/3=ln(x^2/x-4)Homework Equations The Attempt at a Solution I haven't attempted..i...

"If your calculator has overflow issues with this problem, you can use this identity to solve for K: if log(K) = x + y then K = 10x * 10y Problem: log(K) = 127.702 K = 5.04316 * 10127 " Doesn't K = 10127 ? Where are they getting the 5.04316 from? How are they using that specified...

Hi I have to perform a fitting procedure on a semi logarithmic scale but I'm not sure how to weigh the experimental data points. I'm studying the decay of the luminescence of a certain type of crystals and the function I'm using has the form I = \frac{1}{\tau} e^{-\frac{t}{\tau}}...

Homework Statement True or false? ln(1/10) = -\int dx/x The Attempt at a Solution I have no idea where to start on this one. what is dx/x ??

Hi, I'm trying to see why the following theorem is true. It concerns the derivative of the log of the determinant of a symmetric matrix. Here's the theorem as stated: For a symmetric matrix A: \frac{d}{dx} ln |A| = Tr[A^{-1} \frac{dA}{dx}] Here's what I have so far, I'm almost at the...

OK, so paraffin is a hydrocarbon, and is a solid form of kerosene or mineral oil... I wanted to try making my own wax logs for starting our wood stove. Could I take dried out sawdust, mix it with a small amount of mineral oil, suck the moisture out of the "shape", allow for it to dry, then...

Homework Statement A professor is doing a problem on the black board and ends up with the expression \frac{Log A}{Log B} = \frac{2}{3} . He absentmindedly cancels the “log”, making the left-hand side A/B. (A very wrong thing to do!) Luckily, he ends up with the correct values for A...

1. Graphing Carefully: Sketch f(x)= 10(ln(ln(x))/ln(x) accurately using calculus, your calculator, or both to aid you. Make sure to include all vertical asymptotes, as well as local extrema 2. f(x)= 10(ln(ln(x))/ln(x) 3. OK. I might come across as stupid but here goes... I don't...

Alrighty, I know the TI-89 keeps up with date and time. It seems logical that it would somewhere inside the chips and silicon it makes a log of the date that data was inputted...rightttt. I made an idiot out of myself and didn't double check my scan-tron after an exam, my professor jokingly said...

I'm given the following problem. A log sits in the woods with a radius "r". Lazy flea wants to jump over the log with the least amount of velocity necessary. If distance "d" away from the center of the log, and angle theta is the angle of velocity above the horizontal. Find theta, d, and v(min)...

Homework Statement If Logb2=A and Logb49=B, what is logb397, in terms of A and B. This is one of the bonus question in my geometric quiz and i don't remember if the number is 397. I wonder if anyone get this? Homework Equations The Attempt at a Solution here is what i did bA=2 and bB=49...

Homework Statement If Logb2=A and Logb49=B, what is logb397, in terms of A and B. This is one of the bonus question in my geometric quiz and i don't remember if the number is 397. I wonder if anyone get this? Homework Equations The Attempt at a Solution here is what i did bA=2...