Log Definition and 618 Threads

Homework Statement http://i.minus.com/jCH20SF290QIb.png Homework Equations Critical point: when the derivative = 0 or the derivative fails to exist. The Attempt at a Solution I got x = 0 and x = e as critical points. When x = e, the function becomes 0 / e, which = 0...

Homework Statement \int_0^{\infty} \ln \left( \frac{e^x+1}{e^x-1} \right) \mbox{d}x \int_0^{\infty} \frac{1}{x^n+1}\ \mbox{d}x\ \forall n >1 Homework Equations - The Attempt at a Solution I've tried IBP and separating the ln into two terms and failed. I've also tried a...

Homework Statement The full problem is y=e^(x/2) and y=e^(-x) revolved around the x-axis, from [ln6,ln12]. The part I'm struggling with is evaluating 2e^(ln12/2) and 2e^(ln6/2). I am just reviewing for my Calculus 1 final. Homework Equations The Attempt at a Solution...

I'm relatively new to C programming and I am trying to make a program to take and print the natural log of a number input by the user but for some reason my program always returns incorrect answers. For example I entered 1 as my number, and the answer came back as some ridiculously big value...

Yes I know it's a really stupid question, please don't make fun of me. But when they first defined this new function, the integral of 1/x, and had no graph or knowledge of how it looked, how could they know it was a logarithm? More specifically, the logarithm with base e.

Hi. I just saw on wikipedia that natural logarithm has such a property: [x/(1+x)] < ln (1 + x) < x (http://en.wikipedia.org/wiki/Natural_logarithm) Can anyone pls tell me how to prove this? Proving [x/(1+x)] and ln (1 + x) less than 'x' is easy.. But how abt [x/(1+x)] < ln (1 + x)...

[PLAIN]http://img31.imageshack.us/img31/9004/screenshot20111117at720.png Proofs always get to me for some reason. It's like other problems I can do, but when it comes to proofs I don't know what to put. Can anyone show me steps? Thank you

Homework Statement Find the limit of f(x) = x^2 ln(1+1/x) - x x-> ∞ The Attempt at a Solution Not sure where to start, but I take the derivative f'(x) = 2x*ln(1+1/x) +x^2 \frac{ -x^{-2}}{1+1/x} -1 2x*ln(1+1/x) - \frac{1}{1+1/x} -1 the second term goes to -1...

Homework Statement Calculate the following integral: \int_0^a{\left(y-m_1u-c_1\right)\log{\left[u^2+\left(y-m_1u-c_1\right)^2\right]}{\rm d}u} Where "a" is positive Real, "y, c, m" are Reals. Homework Equations \int{\log{\left[u^2+c^2\right]}{\rm...

Firstly, please excuse me if this post is in the wrong section, I couldn't find any "experimental" physics section. Please note that the template is not used since the questions is pretty much descriptive. As part my course, I have one lab session per week. Its duration is one and half our...

It seems this is done randomly, yet it must not be random, there must be some logic to it, but when do you know to do it? What is like a clue or the rules that indicate you can/should take the natural log of both sides of an equation?

Question is: solve for x ln(x+1)-1 = ln(x-1) tried to do it TWO different ways, and neither is the right way, check this out: first attempt: since LN is on both sides , it goes away and you just have variables, that way sucks because then you get 0=-1 , wrong. second attempt: divide...

Homework Statement Hi guys. I'm trying to rearrage an equation using the natural log and I thought I had it correct but am now struggling. I need to rearange it into the form: y=a0 + a1*C. Where a0 and a1 are some combination of the other variables and numbers below Homework Equations...

Any information on the following formula for natural logarithm (I looked in wikipedia and Mathworld but didn't see it). It came from another equation I was working on a bit ago, and I was curious about it as I didn't recall seeing it before (which doesn't mean I haven't), although it reminded...

Hi, I am confused with the results of a seemingly simple simulation that is generating a log normally distributed output. Please see the attached results file. Simulation: I have built a Scratch program that randomly picks six letters from a group of six letters (A, B, C, D, E & E). The...

Homework Statement I wish to find the following integral over the rectangle [-a,a] in u and [-b,b] in v using Mathematica. The constants a and b are positive (and non-zero). The variables x and y are in Reals. A(x,y)=\int_{-a}^a{\int_{-b}^b{\log{\left[(u-x)^2+(v-y)^2\right]}{\rm d}v}{\rm...

Hey, I know the answer to this integral is 2ipi as it was given but I trying to find out how its 2ipi. Here is my working [PLAIN]http://img707.imageshack.us/img707/1681/unledrny.jpg I've been looking at this for ages and I can't work out what I've done wrong thanks,

Is the following relationship true?: \frac{\partial (ln(k))}{\partial P}=\frac{1}{k}\frac{\partial k}{\partial P} I am getting both of these terms from a paper on mineral physics and they seem to use both terms interchangeably. If so, how are these related?

Homework Statement For calc 2 we have to write a formula using integration that will find the volume of any tree log that is cut. Using the picture that is attacked I came up with this equation. The integral from 0 to h of pi*(((R-r/h)x+r))^2)dx. Any ideas about my formula or anything would...

I need help in finding dy/dx or the derivative of these function: 1. y=sin^2(lnx) so d/dx[sin^2(lnx)] I tried following this model of sin^x=(sinx)^2 so d/dx[(sinlnx)^2)]. Then use the chain rule of dy/dx= f'g(g') which is 2(sinlnx)(cos1/x) but I don't think that is right so can you please tell...

Homework Statement I decided to cram these two unrelated question into one post, because they are too small and I don't want to crowd the forum with my many little bitty questions. 1. log(base A) of B= 1/[log(base B) of A] because: if log(base B) of A=C, then B^C=A and so B=A^1/C...

Homework Statement Calculate the following: \int^{-4}_{-6} (x^-1+5x)dx Homework Equations The Attempt at a Solution I've worked this down to ln(-4) + 5(-4) - ln(-6) - 5(-6) =ln(-4)-ln(-6)+10 The answer to the left half (the ln parts) of the equation is undefined, and the...

Homework Statement prove that the series summation from n=3 to infinity of (1/(n*log(n)*(log(log(n))^p)) diverges if 0<p<=1 and converges for p>1. Homework Equations The Attempt at a Solution 2^n*a(2^n)= 1/(log(2^n)*(log(log(2^n))^p)). this is similar to the summation from n=2 to...

Homework Statement Find the integral to the following expression \int\frac{1}{x-1}dx Homework Equations \int udv = uv - \int vdu \int\frac{1}{x}dx = ln(x) The Attempt at a Solution Given the information above, would a correct answer to this problem be ln(x-1) ? If not...

Homework Statement Differentiate, f(x)=71+x/1-x Homework Equations The Attempt at a Solution Working this out, hoping it's right as I was going along, my final answer is 71+x/1-x * (2ln7)/1-x

natural log helpp! Homework Statement ln(x+10)+ln(x+4)=2 2. The attempt at a solution okay so i took it down to (-14+-(14^2 - 4(e^2 - 40))^1/2) / 2 which i broke down to 356 - 4e^2 inside the sqrt. am i on the right track and if so Whats the next step?

Homework Statement [SIZE="4"]log[SIZE="1"]6[SIZE="4"](x+6) - log[SIZE="1"]6[SIZE="4"](x-4) = 3 2. The attempt at a solution 150/36 is what i get which i simplified to 25/6. but the program tells me I am wrong can anyone think of how I am getting this wrong

how to use a log table..and how to find the value of log 1.6 or log 5.62. or any other example.

so I've got this equation down to x*ln(2/x) = 5 Can someone show/point me to a page where I can see how to solve this. I am under the impression it requires some type of ratio computation. thanks!

I used to think I was master of any high school math course until I came across this log equation in a calculus textbook. \log_{2}x + \log_{5}(2x+1) = \ln x I use the change of base to convert everything to one base and then I get down to: (2x+1)^{\ln2} = x^{\ln2\ln5 - \ln5} I have no...

Like the title says, I'm trying to figure out how I can keep an effective log of the stuff I've done in a project. I'm particularly curious about ways to keep a good project log for a long project (i.e. longer than a month). I've tried to do it, but I have a lot of trouble figuring out exactly...

Homework Statement Does there exist a power series expansion of log z around z=0? If so, what is it? If not, demonstrate that it is impossible. Homework Equations [PLAIN]http://img839.imageshack.us/img839/4839/eq1.gif Here is the expansion of log z around z=1. The Attempt at a Solution...

Homework Statement limx->\pi/2(ln sin x)/((\pi-2x)2)Homework Equations The Attempt at a Solution Putting \pi/2 into this equation gives 0/0, however, the limit of this could be 1,0 or infinity, so how would you distinguish between the three?

Homework Statement y = ln | sin x | Homework Equations - The Attempt at a Solution No attempt at a solution, because it's more of a "which part of this is incorrect" question. y = ln | sin x | Would everyone agree that this is equivalent? y = ln \sqrt{(sin x^2)} Then...

In the computer world at least, the symbol ^ is often used for exponentiation. I was just wondering if log has had anything in the multitude of languages out there. It would be nice to see an operator such as "1000¬10=3" instead of writing LogBase10(1000)=3 which is more ugly. I'm writing a...

I am trying to write a computer program that involves finding 2 very large numbers (several thousand digits) and dividing them to get a reasonable sized number. the first number is a value of the gamma function, which can be defined as a product and thus easy to reduce with logs (find the sum...

exam problem : solve exponential withh ... log? This one is killin me! 36^x-6*6^x=-9 please show and explain steps

Homework Statement If (sinx)*(lnx)= 0 over [0, 2pi], then what does x equal? Ok, I know I posted a question similar to this one a few days back, but I need some clarification on something. Below is the work that someone showed me. lnx=sin^-1 (0) lnx=0 Log\hat{}x\check{}e=0 (If you...

Hello I'm trying to plot log as part of an equation in mathematica and it does not seem to be working for me. for example I'm using Plot y = 25x / log10 (x) - 50x I'm just experimenting with different numbers and formulas to see what happens to the log curve...

Homework Statement Two ropes are attached to a log that is floating in the water. A force of 80.0 N is applied to one rope and a force of 60.0 N is applied to the other rope, which is lying at an angle of 40° from the first rope. What is the net force on the log? We know that the angle...

Homework Statement This is not a specific problem that I must complete, but I realized that I forgot how to solve these style problems! Homework Equations The Attempt at a Solution For instance, off the top of my head: 3e^{x+1}=e^{x+2} I would divide both sides through by 5 to get...

Solve the equation log (little 3) X + log (little6) X = 2 the answer is 3.9 Here is what I try log (little 6)x = log (little 3)x/log (little 3)6 = log (little 3) (x-6)log (little 3)x + log (little 3) (x-6) = 2 log (little3) (x(x-6)) =2 log (little3) (x^2-6x)=3^2 x^2 -6x =9 x^2-6x-9=0 x= 7.2...

Hello! I am trying to solve the partial derivative 'P' http://www.flickr.com/photos/61865210@N07/5757168138/ , which is part of a larger equation: http://www.flickr.com/photos/61865210@N07/5757300018/ (Sorry, can't seem to display to pictures, using insert image) Someone told me that solving...

I was wondering if there could be more identities than i have read. I was doing questions on log and found many questions in this form:- (loga b)2 (loga b)(loga c) This is not my homework but i require these identities to solve the questions. Please someone tell me how to solve these...

I'm having a simple problem with simplifying of logs. Given the input : FullSimplify[8 Log[m1] - 8 Log[m2] + 4, m1 > 0 && m2 > 0] FullSimplify[8 Log[m1] - 8 Log[m2], m1 > 0 && m2 > 0] I get out: 8 log(m1)-8 log(m2)+4 8 log(m1/m2) So for the second command it combines the logs...

Homework Statement it wants the sum of all solutions 2 different problems 1. and 2. 1. 2^x + 2^(x+1) + 2^(x+2) = 2^6. 2. 8/(3^x +2)>=3^x >= meaning equal or greater than 3^x Homework Equations should i come up with a summa equation? The Attempt at a Solution i...

Homework Statement 9^x-5*3^X+6=0 Homework Equations I have no idea how to solve this i suspect there is a theory that I am not familiar with involved. want real numbers. The Attempt at a Solution i thought about moving the 6 to the otherside and doing log on both but you can't...

Please help i have these two questions and i am Stuck! Question 1 The linear equation you have found (y=.771x+1.609) is in the form of y= mx +c. it should be however more appropreiatly be considered as being in the form, lny = mx + lnA. by using appropriat logarithmic and exponential laws...

Currently working on a high school physics assignment. I need help on some questions, just so that I know I am in the right direction. I am not here to get you guys to do my homework for me. But anyway, the following questions are about a log fume ride, and the acceleration and velocity of a...

\int_{-b}^{-a} \frac{dx}{x} = ln(x)|_{-b}^{-a} What is this equal to? I don't know how to proceed. Please help. Thank Alan