Logarithm Definition and 339 Threads

Homework Statement http://img213.imageshack.us/img213/4474/scan0001ha.jpg

Hi all, Do you know how to solve the following inequations? \ln \left( {\frac{{x + a}} {{x + b}}} \right) \leq cx + d \ln \left( {\frac{{x + a}} {{x + b}}} \right) \geq \frac{{x^3 + cx^2 + dx + e}} {{ux^2 + vx}} a, b, c, d, e, u, v are constants. x is a variable. Can you suggest...

Homework Statement Verify the formula logbx = logax/logab for a, b > 0 Homework Equations The Attempt at a Solution I don't even know how I would go about starting this...

How many integers will satisfy x in the inequality: 1< \log_{3}({\log_{2}{x})}< 2 Note: The log there is not multitplied to the other log. The log there I think is read like this, logarithm of logarithm of x to the base 2 to the base 3. What can be the solution or technique for this...

Hello, I made a mistake in the title of this thread and this question is on general logarithms; loga(aloga(x)) = loga(x) ==> aloga(x) = x Can someone enlighten me on why loga(aloga(x)) simplifies to loga(x)? Can someone prove why this is true? Futhermore, why does this imply that...

This equation specifies displacement x in terms of motion time t (starting from rest). x = \tau g\left(t + \tau e^{-t/\tau} -\tau\right) where tau = m/b is the system time constant of a mass m suspended from a mechanical braking device with rectilinear damping constant b and g is standard...

How does (ln(x))^(1/x)=ln(x^(1/x))? A friend told me this was a true statement but could'nt prove it. If that isn't true, then how would you find the lim x->0 of (ln(x))^(1/x) using L'Hospital's Rule?

Homework Statement Positive integers a and b, where a < b, satisfy the equation : ab = ba By first taking logarithms, show that there is only one value of a and b that satisfies the equation and find the value ! Homework Equations logarithm The Attempt at a Solution I know the...

Homework Statement e^z = e e^z = e^-z Homework Equations they are the first 2 questions on my homework and my book is so bad i don't even know how to get the right answers, I've been online for over an hour I'm i'm sure they are easy. The Attempt at a Solution ffirst one just...

I read the following expression in a book: \int_{-\infty}^{\infty} \dfrac{1}{t(1-t)} \log \left| \dfrac{t^{2} q^{2}}{(p-tq)^{2}} \right| ~ dt = - \pi^{2} p and q are both timelike four-vectors, so p², q² > 0 This integral was solved by using the identity \lim_{s \to \infty}...

hi, can you evaluate ln(f(x)) in your favorite cas (where x is a zero of f(x) )? what is the result?

First of all, greetings to the scientific community here at Physics Forums. The following set of equations is given: y^(x-3y) = x^2 x^(x-3y) = y^8 With the next assumption given: x-3y is unequal to (-4). My attempt was to isolate the y variable in both of the equations so that i will...

Homework Statement Hi everyone I need help for this problem : If 2*\log_2 (x-2y)=\log_3 (xy) , find \frac{x}{y} Homework Equations \log_bx = \frac{\log_ax}{\log_ab} The Attempt at a Solution 2*\log_2 (x-2y)=\log_3 (xy) \log_2 (x-2y)^2=\log_3 (xy) \frac{\log_2...

Hello, Can we interchange the natural logarithm "ln" operator and the integral operator? Regards

does anyone know how to calculate (in the sense of distribution) the Fourier transform of f(x)= ln|x| that is to obtain the integral \int_{-\infty}^{\infty} dx ln|x|exp(iux)

Homework Statement Hey all, I just need some help remembering my basic simplification rules. Can the expression eC*ln(x) be simplified anymore. It would certainly help out an integral I'm working on but I don't remember my simplification real well. Homework Equations elnx=xThe Attempt at a...

Suppose X\in\mathbb{R}^{n\times n} is orthogonal. How do you perform the computation of series \log(X) = (X-1) - \frac{1}{2}(X-1)^2 + \frac{1}{3}(X-1)^3 - \cdots Elements of individual terms are ((X-1)^n)_{ij} = (-1)^n\delta_{ij} \;+\; n(-1)^{n-1}X_{ij} \;+\; \sum_{k=2}^{n} (-1)^{n-k}...

I am trying to explore a number of things regarding the entropy of random strings and am wondering how a character set of random size would affect the entropy of strings made from that set. Using the following formula, I need to take the log of a discrete random variable H = L\log_2 N...

What difference will it make?

Homework Statement 1) Solve the equation using the exponential form of the equation. Log2(2-5x)=7 2) Rewrite as a single logarithmic expression: 3log x +(1/2)log z Homework Equations The Attempt at a Solution 1) I have no idea how to solve this. 2) I know that two logarithms multiply to...

I know that there is a year old thread that has just been resurrected that is slightly on this topic, but I had a question that I thought might merit a new thread. I'm working with my Calculus book here, and I'm working on the chapter called, "Logarithmic Functions from the Integral Point of...

Homework Statement Let I be the identity matrix, and let N be a nilpotent matrix order k. Then the matrix exponential function is defined as: exp(N) := I + N + (1/2!)*N^2 + (1/3!)*N^3 + ... + (1/k!)*N^k Similarly, we may define the matrix logarithm as the function -log(N) := I - N +...

hello, I was trying to figure out what will be the y value for this equations: 1 - e^-0.15*10^-5*y = 0.1 Could somebody help me in this?? The answer is supposed to be 70,240. thanks.

Can someone please tell me how to expand \ln(x + \sqrt{1+x^2}) for small x? I'd like to retain terms at least up to order x^5. Thanks!

Hi! Does anyone know what a branch-cut singularity is? I have been trying to understand its importance in physics, but I got lost. I would guess that a singularity in physical context should mean that the value of a function should become very big near that singularity. But if we take complex...

Homework Statement log2(x+2)=log2x2 -log base 2(X+2)= log base 2 (x2) The Attempt at a Solution I know the answer is supposed to be -1 and 2, but I get the wrong answer every time I try. I tried bringing log2x2 over to the other side and then got log2(2/x) which got me nowhere...

Homework Statement Rewrite the expression as a sum, difference or multiple of logs. log55x2 Homework Equations The Attempt at a Solution log55x2 = 2log55x = ...

Homework Statement \displaystyle\int\left(\dfrac{\ln x}{x}\right)^2 dx 2. The attempt at a solution I tried letting u=\ln^2 x and dv the rest and I also tried dv=\ln^2 x dx and u the rest. It won't work out.

Homework Statement Hi. I want to solve: \frac{d\ln(-x)}{dx}. When using the chain rule I get: \frac{d \ln(-x)}{dx} = \frac{d\ln(-x)}{d(-x)}\frac{d(-x)}{dx} = -\frac{d\ln(-x)}{d(-x)}. But how do I find the last derivative? I know by experience that it is -x-1, but how is the derivation...

I have been working on a solid state physics homework problem, and I have gotten the answer down to an integral that I am unsure how to do by hand. I can plug it into Mathematica, and I receive the correct answer (I am asked to show something) but I would like to know how to do this integral by...

Homework Statement This one has has me pretty lost, I'm not at all sure what to do, I've tried a couple of things. I have to find x. 2(x-1) = 5(73x) Homework Equations Logarithm laws? The Attempt at a Solution (did multiple attempts but my most reasonable to my account) 2(x-1) =...

Homework Statement Find x in the following equation (ln 64 / 2) + ln x = ln 18 - ln x The answer should be x = 3/2 Homework Equations Logarithm laws ln m - ln n = ln (m/n) The Attempt at a Solution I tried two methods: (ln 64 / 2) + ln x = ln 18 - ln x ln 32 + ln x = ln 18...

Hello, I understand the current concept of the characteristic however there either is a mistake in my answerbook or I made a mistake log15 850 = 850(1/15) = 1.568 The characteristic should be 1 and the mantissa is 0.568 -- My answer book says it's 2. I have done all my other exercices...

Homework Statement It was found that the percentage of the carbon-14,P, contained in the bones of an animal n years after it has died is given by P = 2^{-kn} , where k is a positive constant. The percentage of carbon-14 contained in the bones after the animal has been dead for 5668 years was...

Homework Statement Prove: 1/log3a + 1/log4a = 1/log12a Homework Equations ay=x Logarithms rules (addition, subtraction, power, etc.) logax=logbx/logba The Attempt at a SolutionLeft Side: 1/log3a + 1/log4a =log3a+log4a/log12a (via common denominator) The problem is how to add logarithms...

Homework Statement Express 2log_{2}X=1+log_{a}(7X-10a) find x in terms of a. i wondering if there is other methods to solve aside from completing the sq. Homework Equations The Attempt at a Solution Homework Statement Homework Equations I got x²-7ax+10a²=0...

Got no clue .. need some clues

Homework Statement Write expression as a logarithm of a single quantity and then simplify if possible. (1/4)[log (x²-1)-log (x+1)]+3log x Homework Equations The Attempt at a Solution I got (1/4)log(x-1) + 3log x so far

Hello! Run into trouble...again. This concerns the inverse function of a logarithm If a function maps x on to logax, then the inverse maps logax on to x. So, f(x) = logax, can be presented as y=logax; therefore, x=ay. The book states that the inverse is ax, why is this the inverse? I tried...

Hi. I know that for real numbers log(z)=-log(1/z) is this also true in general for complex numbers?

I am not a physics or math student ,but i am interested in physics i want to understand the nature So i started studying physics my main source is internet .So i need help from people like U . 1.what is limits how and where it is used ? 2.what is logarithm how that table is made? 3.what...

I'm taking a complex variables course, and I'm really stuck at it, I've never felt this way in any math course before :S, I'm starting to get angry. Anyway here is the problem, I hope someone can give me a hand. I believe this is a basic and simple problem in the subject... Homework Statement...

I was wondering if the Golden ratio base (phinary system) has any use somewhere and if arithmetics with it is easy? I programmed a surprisingly simple algorithm to calculate the logarithm yielding digits in base phi using nothing more than 2 multiplications/divisions per result digit. Can it...

log8(9y+14)=6x6-11 9y+14=86x6-11 ln(9y+14)=ln86x6-11 ln9y+ln14=(6x6-11)ln8 ln9y=(6x6-11)ln8-ln14 y=((6x6-11)ln8-ln14)/ln9 is this equation correct??

(For those values of x for which a solution exists), solve the following equation for y 3e3y-6 = 2x2-1 What does it mean by the values of x exists??

Calcule: ln\frac{273}{263}

i am student of ladoke akitola university of technology ogbomosho oyo state Nigeria . help me on this question log^18-log^10=19

Well I read in a book that: \DeltaG= RTln (K) (Where K is the eqm const) H "K" is not necessarily dimensionless so how can we take a log of "K"?

i have a problem please help http://img373.imageshack.us/img373/3052/index1bd9.gif Who can solve this for me?!

I was recently doing some problems with Entropy, and came to the startling conclusion of incorrect units for most of my answers! One problem, for example--was to calculate the change in entropy of a given sample as it gained heat per temperature. \Delta S=\int^{f}_{i}\frac{dQ_{r}}{T} The...