Log Definition and 632 Threads

Has anyone seen this identity: g^{ab}\nabla g_{ab}=\nabla ln|g| I've seen it used, but want to figure out where it comes from. Does anyone know a name or have any ideas??

A rope is tied to a 97.8 kg log. When you pull on the rope with a horizontal force of magnitude 706 N, the log moves at constant speed. a) Find the magnitude of the resistive (frictional) force acting on the log. You may assume the frictional forces acting on the log is constant. N b)...

Hello, I am interested in the average behaviour of the log of a function. I know the average of the function over the range of interest: F = \frac{1}{(b-a)} \int_a^b f(x) dx. I also know that f(x) is convex and bounded from below by 1. I want to know the average \frac{1}{(b-a)}...

Question asked to find the units of k after you find the porpotionality statement i ended up getting t\propto\frac{\sqrt{h}}{d^2} so i turned that into an equation and end up with t=k\frac{\sqrt{h}}{d^2} solved for and found it on average to be 30 now the question is asking what the...

Homework Statement Find the limit of (tanx)^cosx as x-->infinity Rearrange the equation so that you can use L'Hopital's rule for the form of (infinity/infinity) The Attempt at a Solution I did ln(tanx)^cosx = cosxlntanx I know the limit of tanx as x-->infinity is pi/2 the limit of cosx as...

I've got a simple question that's been bugging me for a while. I think I know where the problem is, I'd just like a formal mathematical reason why I can't say this: \ln{(-1)}^2 = \ln(1) = 0 That part is fine...but then: \ln{(-1)}^2 = 2 \ln(-1) = 2 (i \pi) when they should...

[SOLVED] Help a newbie! Hey everyone. This will be my first post. A little background info: I have a bit of math anxiety due to doing very poorly with it in school despite a bit of effort. I had finished college in May with a degree that required only Statistics. My last year, I had...

Homework Statement See image Homework Equations M = log(I_i / I_o) The Attempt at a Solution See image

Roshambo is the name for a popular two-person hand game. It may also be referred to as Paper, Rock, Scissors. Rock blunts scissors, scissors cut paper, paper folds around rock. Nature plays it too. But instead of paper it uses logs: Log folds around rock...

Homework Statement Let f be the function given by f(x) = ln [ x/ (x-1)] (a) What is the domain of f? (b) What is the value of the derivative of f at x = -1. (c) Write an expression for f^(-1) of x, where f^(-1) denotes the inverse function of f. The Attempt at a Solution a. x / x-1...

Homework Statement A hearing aid increases the sound intensity level, thereby allowing a person to hear better. For the following decibel increases, by how much does the intensity of sound increase? a)30dB b) 22dB Homework Equations \beta=10log (I/Io)The Attempt at a Solution I substitute...

can someone please explain this to me?

Homework Statement Solve the equation log base 7 (7x+8) = log base 7 (7x+3) Homework Equations I don't think you use equations for this, just the properties of logarithms The Attempt at a Solution I thought since they have the same base you could set the parts in parenthesis equal to each...

Homework Statement Given a^2+b^2=47ab provehat log((a+b)/7)=1/2(loga+logb) The Attempt at a Solution I am assuming it is using multiple log properties... idk how though :|

[SOLVED] log a 3.5= ? given log a 2= 1.8301 and log a 7= 5.0999 what is log a 3.5=? Thanks!

double log scale - please help I am trying to find/create the equation for a straight line on a double logarithmic scale graph - what is the format of the equation or how do I do this using data points from the graph.

1. Convert to logarithmic function: e^3=0.0498 3. ln(-3)=0.0166 is my guess

Homework Statement Find y' y=ln(x^2 + y^2) Homework Equations d/dx ln(u)= 1/u du/dx The Attempt at a Solution y' = [1/(x^2 + y^2)] (2x + 2y) y' = (2x+2y)/(x^2 + y^2) But my book says the answer is 2x/(x^2 + y^2 - 2y) How can that be?

It seems to that i went wrong way. Homework Statement \int \frac{arcsin(e^x)dx}{e^x} The Attempt at a Solution =-\frac{arcsin(e^x)}{e^x}+\int \frac{dx}{\sqrt{1-e^{2x}}} \int \frac{dx}{\sqrt{1-e^{2x}}}=\frac{x}{\sqrt{1-e^{2x}}}+\int \frac{xe^{2x}dx}{(1-e^{2x})^{\frac{3}{2}}}

**Im helping a friend go through this problem, so "the answer will be shown eventually" because I am editing as we go through. Homework Statement 2^{x-1}=25Homework Equations All Log/Exponent Formulas, they'll be shown as we go. The Attempt at a Solution There are various ways of approaching...

Homework Statement log_u (5) = a; log_u (27)=b; log_u(32)=c what is the numerical value of u^(2a+(1/3)b-(2/5)c) Homework Equations The Attempt at a Solution Can you do (u^2a * u^(b*1/3) ) / ( u^(c*-2/5))) and then do log_u of the whole thing from here can you make it ((u^a)^2 *...

Homework Statement Prove that f(n) = n * log (n) is O(n(1+sqrt(n))). Homework Equations n/a The Attempt at a Solution I really don't know what to do else I wouldn't be here :? Some hints would be appreciated!

Hello Im studying an ATS equipment known as an ILS. One of the formulas to determine the DDM is : E2 = E1 log-1(db/20) When I try entering log-1, the calculator displays Math Error. What am I doing wrong? Thanks for the help in advance

Homework Statement 2^x=1500. solve for x. I need to know the key strokes on my scientific calculator. If I push log, it assumes log base 10. I need base 2. Homework Equations The Attempt at a Solution

Homework Statement Solve for x: log(x+5)= log x + log 5. Homework Equations log a + log b = log (ab) The Attempt at a Solution log (x+5)= log (5x) x+5= 5x 4x=5 x=5/4 However, my question is: When you make the logs to the power of 10, to eliminate them, do you always...

Hi, I've been trying to work out: loga(2+x) = 2 + logax This is as far as I can get: loga(2+x) - logax =2 so: loga((2+x)/x) =2 loga((2+x)/x) =log100 (I'm not even sure where I could go with this one though). Relevant equations include: log x +log y = log xy log x - log y = log x/y...

Problem: If 2^{x}=3, what does 3^x equal? I solved this by taking the log_{2} of both sides. However, the book's solution involves taking the natural log of both sides. Can someone show me why that would work? I don't get what the x power changes to a x term. The natural log is base 10 right?

Homework Statement I'm supposed to evaluate the following series or show if it diverges: SUM (sigma) log [(x+1)/x] Homework Equations Drawing a blank...:confused: The Attempt at a Solution I'm unsure how to start this. We've gone over all sorts of tests for convergence (ratio, comparison...

I'm having real problems integrating a natural log. The problem I have been set is (where S = integration sign) S (x - 2) Ln(3x) I'm trying to use the integration by parts rule but keep getting the wrong answer and I think it might be to do with the natural log. I have used f(x) =...

If we have a function of the form Ln(ax) Is it the case that the derivative is simply 1/x no matter what the initial value of 'a' might be? Or do we take into account 'a' in some way The thing i need clarifying is this... If we have Ln(3x), the derivative is 1/x, but the integral of...

Hi. Could someone please help me with the following questions? I'm totally stuck so any feedback would be really appreciated. I'll post the questions one at a time. Express as single log. functions: (i) ln (x + 1) - 3 ln (1 - x) + 2 ln x I got up to ln ( (x + 1) / (1 - x)^3 ) / ln...

Homework Statement the indefinite integral of (1+lnx)^(1/2)/(xlnx) dx Homework Equations n/a The Attempt at a Solution There aren't any x^2 in the root sign, so I don't think it can be a trig substitution. The only logical u sub I see is to let u=lnx. In that case, du=dx/x so the...

What is Log e ? (log sub e) Where would i find it on a calculator?

Homework Statement (Idk how to put in the equation to make sense, therefore it is at the link below) Homework Equations The Attempt at a Solution Here is all I have done. Something just isn't right...there should be 3 answers (in the back of the book) because there is a cube...

Basic log question, completely lost! :( Homework Statement Prove that y = a(1+b)^t is equivalent to ln y = a+bt Homework Equations The Attempt at a Solution i'm really confused with how they could possibly be equal. y = a(1+b)^t t = ln y/ln a(1+b) ln y = t x ln (a+b) ln y...

Can you get logarithms of imaginary numbers? The reason I was wondering is because integrating 1/(1+x^2) WRT x. I know the answer is arctan(x), but how about breaking it into partial fractions by doing 1/(1-ix)(1+ix)?

Homework Statement Solve the equation: 2^x multiplied by 4^(x + 5) = 4^(2x - 1) Homework Equations The Attempt at a Solution 2^x multiplied by 2^2(x+5)=2^2(2x-1) x(2x+10)=4x-2 2x^2+10x=4x-2 and that's as far as i could get before I was completely stuck. But this could be...

Homework Statement Solve for Y in terms of X Homework Equations 2log_5X/ log_53 - log_5Y = 2 The Attempt at a Solution I know all the properties of logs, i just don't know how to apply them to this problem. The answers in the book are . y = 1/25x^2/log_53 When i am...

Homework Statement the question asks to graph the equation: (don't know how to use latex sorry) f(x) = log5 (x) + 3 where the 5 is the base Just for my curiosity what would the exponential equation be? I can graph it, just can't get the exponential form Tell me if this should go in the...

Here is a silly question from our book, that seems to be a pain to solve: ------------ Solve the following equation: 59^x \equiv 63 \ \text{mod 71} ------------ The idea is to use the discrete log (or index). Note that 7 is a primitive root mod 71. The two books I have looked at...

I was working on an experiment for the vapor pressure of water and I have the following formula ln (p) = -L/(RT) + ln (p_o) L=heat of vaporization of water R=Molar gas constant T=temperature in Kelvins I have some data points for the pressure p in units of mm Hg, when I take the...

Can someone explain to me when to use natural log or common log? I understand that natural log gives creates a base e and the common base 10 but i don't understand why there are 2 different ones.

Hi, To solve the following d.e.: xdy-ydx = 0 1 you get ln(y)-ln(x)=C 2 no clearly you can simplify to: ln(y/x)=c 3 which after taking exponentials gives: y=Ax where A=e^c 4 however what interests me is if you do not simplify...

Homework Statement log base 5 cube root 25 equals what? Homework Equations I know that the answer is 2/3 because it is in the back of the book The Attempt at a Solution log base 5 = 25 to the 1/3 so 5 to the what = 25 to the 1/3 How do I get 5 to the 2/3 equals 25 to the...

Hi, I come from an engineering background and so have not studied analysis (sadly). I need to figure out the following. How does: 1.) x^y*|ln(1/x)|^m behave for any m given y<0 as x-> infinity 2.) x^y*|ln(1/x)|^m behave for any m given y>0 as x-> 0 The way I see it in the...

Here we go again. Another layer has been added to the Bush administrations unprecedented record of secrecy. http://www.guardian.co.uk/worldlatest/story/0,,-6325579,00.html

How would one go about solving for C in the following equation? log ( A - B - C ) = -C + A + B I have done this... log ( A - B ) / log ( C ) = -C + A + B Then... C + ( log ( A - B ) / log ( C )) = A + B But I am just shooting in the dark really. Where would one go from here...

Homework Statement find dy/dx for y=ln(sec^(2)x) Homework Equations none The Attempt at a Solution 1.)1/(sec(x)^2)*dy/dx sec(x)^2 2.)tan(x)/sec(x)^2 3.)i put it in terms of sin and cos... sin(x)/cos(x)*cos(x)^2/1 4.)i canceled the cos(x) in the denominator and came...

I have the problem 3e^(x+2) = e^(-x) and I need to find X. It's been a while since I've looked at any Calculus 2 stuff so I am not sure on what to do here. I take the natural log of both sides LN(3e^(x+2) =LN(e^(-x))= (x+2)ln3e = -xlne So (x+2)Ln3e= -x Where do I go from here?

Homework Statement When you walk along a floting log in water, why does it move in the opposite direction? Is it because of the friction from you walking pushes the log in the opposite direction, or is there something else?