Logarithmic Definition and 362 Threads

Homework Statement Hello, I have a set of data that is grouped into bins. The bin sizes increase logarithmically by 10% (1.1 x the previous bin). Homework Equations Bin Mean Radius Frequency 1.03 4924 1.10 9938 1.21 14009 1.32 12269 1.44 15813 1.58 18723 1.74 21471 ...

what is the integral of the function 1/lnx?

the idea is let us supppose we have a well behaved theory where only logarithmic divergences of the form \int_{0}^{\infty} \frac{dx}{x+a}=I(a) for several values of 'a' occur , then would this theory be renormalizable ?? , i think QED works because only logarithmic divergencies appear ...

Homework Statement The amplitude of a torsional vibration decreases so that the amplitude on the 100th cycle is 13% of the the amplitude of the first cycle. Determine the level of damping in terms of the logarithmic decrement. Homework Equations The Attempt at a Solution Is this...

The amplitude of a torsional vibration decreases so that the amplitude on the 100th cycle is 13% of the the amplitude of the first cycle. Determine the level of damping in terms of the logarithmic decrement. Is this simply ln(100/13)= 2.04 or ln(13/100)= -2.04?

log9 (p) = log12 (q) = log16 (p+q) What is q/p? 9^x + 12^x = 16^x calculate x (4/3)^x = q/p I guess that would work if I'd know how to solve that equation (without using a calculator), unfortunately I don't... 3^(2x)+4^x*3^x = 4^2x

Hey guys, I have a potentially (no pun intended...ok maybe a little) stupid question. People often use log potentials to model galaxies with flat rotation curves and things and I'm currently using it to model a galactic potential for some simulation work. However none of the sources i have...

Homework Statement I need to find N: {[pi^(N+1)] / (N+1)!} . {1/2^N} <= 10^-5 Homework Equations The Attempt at a Solution I'm really struggling with this, i think taking logs is involved, but i can't seem to find a value of N. Any help?

Homework Statement http://img142.imageshack.us/img142/8564/76203773.jpg Homework Equations I need to somehow express the above equation in terms of logax, logay,and logaz.The Attempt at a Solution I got the answer loga * [ |x|*sqrt (x)] + loga * [|y|] - loga * [z] But I'd just like to get...

\frac{2\sqrt{3} - ln(2+\sqrt{3})}{4} Given that the x co-ordinate is ln(2+ \sqrt{3}) which I worked out in the first part of this qusetion given that at A there is a maximum turning point (so maximum turning point means dy/dx = 0), but I'm not sure that helps in this part of the question y=...

Homework Statement The half-life of a radioactive substance is 194 days. How many days will it take for 80% of the substance to decay? Homework Equations The Attempt at a Solution I had to make 1/2n=1/5. I did this by finding log25=n. After this, I needed to only multiply by...

Homework Statement \int\frac{ds}{s^2} Homework Equations None really...I suppose \int\frac{a}{bx + c} = \frac{1}{b}ln.a.(bx + c) The Attempt at a Solution Pretty much, using the formula above gives you: ln(s$^{2}$) But I was thinking, if you rearrange \frac{ds}{s$^2$}...

Homework Statement Find the value of x Homework Equations log x - 1/2log(x-1/2) = log(x+1/2) - 1/2log(x+1/8) The Attempt at a Solution used the log a + log b = log a*b & log a - log b = loga/b and got a cubic equation 4x^3-8x^2-4x-1 = 0 but the answer in the book is x=1

Homework Statement (e^x)^2-5(e^x)=0 Homework Equations I've reviewed my logarithmic rules, but I cannot get to the right solution. I should be trying to get one e^x on each side so that I can take the ln of both sides and end up with a simple algebraic process to solve. The Attempt...

Homework Statement Hey guys, this is my first post and of course first question to ask of calculus Alright well I had this test and we had this very difficult question that I could not solve, it was in the hardest section. The question is as follows: A projectile thrown...

Hello All, I am working on a program that produces plots that use a logarithmic scale on the X-Axis (for showing decade frequency ranges). The Y-axis can have any arbitrary value and I'm not thinking about that at this point, but here is my question. Say, for simplicity that every Y-value...

Hi, I have the following equation: \Theta = log \left(\frac{\Pi}{1-\Pi}\right) I want to re-arrange it for \Pi Here's my attempt: \Theta = log \left( \frac{\Pi}{1-\Pi}\right) \Theta = log \left( \Pi \right) - log \left(1-\Pi \right) exp^{\Theta} = \Pi - (1-\Pi)...

Homework Statement I can't seem to get my head round this problem, I know how to use the 'change the base rule' log_2 x + log_4x = 2 \frac{logx}{log2} + \frac{logx}{log4} = 2 why is this not correct ??

Homework Statement Sove cosz=2 Homework Equations The Attempt at a Solution I need to solve this, but am not quite sure how. I was told to use log.

Use logarithmic differentiation to find: a.) d/dx of [(sin^-1(x^2)*sinh^-1(x^2))/(sin^4(x^2))] b.) d^2/dx^2 (sech^-1(e^(2*x))) work shown for a: let y= [(sin^-1(x^2)*sinh^-1(x^2))/(sin^4(x^2))] taking the natural logarithm of both sides: ln y= ln...

Use logarithmic differentiation to find: a.) d/dx of [(sin^-1(x^2)*sinh^-1(x^2))/(sin^4(x^2))] b.) d^2/dx^2 (sech^-1(e^(2*x))) work shown for a: let y= [(sin^-1(x^2)*sinh^-1(x^2))/(sin^4(x^2))] taking the natural logarithm of both sides: ln y= ln...

Homework Statement I need to find as much as a complete logarithmic formulas worksheet or tutorials I have not been in school for atleast 2 semesters and the class I am taking right now makes use of the basic logarithmic functions, not to complicated from what the teacher has told us. I do...

y = (sin2x)3(x4-4x)6 divided by (cosx) + e3x i came out with an answer y' = (sin2x)3(x4-4x)6divided by (cosx) + e3x [3cot2x + 24x3-24 divided by x4-4x + Tanx + 3x could someone tell me if I am right? i don't know if this is what I am supose to do, if you want me to write out...

Homework Statement Find a formula for f^(n)(x) if f(x) = ln(x-1) Homework Equations The Attempt at a Solution Not completely sure what the problem is asking for, any suggestions? Also, another quick question. If I am trying to graph a problem using a ti-89 that shows two tangent...

Homework Statement Use logarithmic differentiation to find the derivative of the function. Homework Equations y = (sin(x))^(ln(x)) The Attempt at a Solution I guessing the first step is raise both sides to "e", but so far I have only completed problems by taking the natural log...

Homework Statement Resolve the following equation: log2 x + log2 [(x-3)/5)] = 3 Homework Equations Logarithmic laws: logc m + logc n = logc mn The Attempt at a Solution Restriction: (x-3)/5 > 0 x-3 > 0 x > 3 Resolution: log2 x + log2 [(x-3)/5)] = 3 log2 x[(x-3)/5)] = 3 log2 [(x2 - 3x)/5x]...

Hello again.. Homework Statement I I have to change this to one term only, the valid answer is: log (x + 1) The term is: 2 log (x2 - 1) - log (x + 1) - 2 log (x - 1) Homework Equations Logarithmic laws: x log n = log nx log m - log n = log (m/n) The Attempt at a Solution I...

Homework Statement I have to take the following equation and make it one single log [log_{2} 9/log_{2} 10] - log 3 The answer is equal to: log 3 I usually know how to do this however I have no clue in this case, I have the answer however. Homework Equations None? log x - log y...

hello.. i don't know where to start solving this problem can you please help me? log phi of x (v)= e-2vx^(1+v/sq.rt.x)2x-1. please..I really need your help. Thank you so much.

Just wondering if someone can tell me if I got this correct. It was a problem on my midterm a month ago and I am going over the probs I got wrong, and I don't know the correct answers. Homework Statement 4(x+1)= 8(x-1) Homework Equations The Attempt at a Solution log 4(x+1) =...

Exponential Equation with x on both sides Homework Statement 18x^2=6e^(2x) Homework Equations I don't know any for the step I got stuck on. The Attempt at a Solution 3x^2=e^2x ln3x^2=lne^2x 2ln3x=2x ln3x=x

Hello everyone! I have two precalculus problems that are from an assessment today that I had some great trouble with. I wrote the objectives below, followed by the problems themselves. Any help is greatly appreciated! Homework Statement 1. Solve exponential and logarithmic equations when...

I'm having a lot of trouble on this worksheet I have, I've got most of the 32 questions except for about 5. I won't type out all the laws of logarithms as I assume that anyone coming in here to help me already knows them. So here are my questions (By the way, I've done work for them I just...

Homework Statement Ae^dt + Be^ft + Ce^gt + De^ht + ... = Y Where A-Y and d,f,g,h, etc are constants. Homework Equations Logarithmic identities... ( log(AB) = log(A) + log(B), log(A^x) = x log A, etc) The Attempt at a Solution I could do this if there was only one term on...

Another problem I'm not sure of :( find \frac{dy}{dx} for the function xy^{2} + x lnx = 4y my answer y^{2} + x2y \frac{dy}{dx} + lnx + x (1/x) \frac{dy}{dx} = 4\frac{dy}{dx} x2y \frac{dy}{dx} + \frac{dy}{dx} - 4\frac{dy}{dx} = -y ^{2} - lnx \frac{dy}{dx} ( x2y - 3) =...

f(x) = ln (12x-5/9x-2) f'(x) = (4/3) (1/ln10)(9x-2/12x-5) Is this correct??

3e3y-6 = 2x2-1 ln3e3y-6=ln2x2-lne ln3e3y-6=ln2x2/lne 3e3y-6=2x2/e 3e3y-6*e=2x2 e3y-6=(2/3)x2 3y-6=ln((2/3)x2) 3y=ln((2/3)x2)+6 y=(1/3)ln((2/3)x2)+2 I wonder the answer is correct, the question is asking about the equation of y.

Homework Statement x=\frac{1+\frac{f(x+1)}{1!}+\frac{f^{2}(x+1)}{2!}+\frac{f^{3}(x+1)}{3!}+...}{1+\frac{f(x)}{1!}+\frac{f^{2}(x)}{2!}+\frac{f^{3}(x)}{3!}+...} f(x) is a twice differentaible equation. 1. Find the possible values of x when; f(x+0.5)<f(x-0.5) 2. Find the possible values of...

Homework Statement For x>1, find the minimum possible value of 2 log_{2}x-log_{x}(0.01) The Attempt at a Solution Greater the value of x, greater is the value of expression. Right? I tried to differentiate it, but it was no help. The derivative becomes zero when |log x|=\sqrt{log 2}...

Homework Statement f(x)=(((x^7)+3)((x^3)+2)) / (((x+3)^2)((x^6)+5)) Find f'(x) Homework Equations d/dx lnx = 1/x d/dx ln(f(x)) = f'(x)/f(x) The Attempt at a Solution ln(f(x)) = ln((x^7)+3) + ln((x^3)+2) - ln((x+3)^2) - ln ((x^6)+5) f'(x)/f(x) = (7x^6)/((x^7)+3) +...

Homework Statement Find the maximum and minimum values of the function F(x)=ln(x/(x^2+1)) on the interval (0,10] Homework Equations d/dx[lnu]=u'/u The Attempt at a Solution f'(x)=(1-x^2)/[(1+x^2)x] f'(x)=0 when 1-x^2=0 1=x^2 x=1 which is the maximum f(1)=-.693 what do I use...

Question: Find derivative of f(x)=((x^2)(x^3))/((x^4)(x^2)) Attempt: ln f(x)=(lnx^2)+(lnx^3)-(lnx^4)-(lnx^2) Can someone tell me what I have done wrong so far? Thanks

O(1) is constant O(log n to the base 2) is logarithmic O(n) linear how would you prove that constant is a subset of logartihmic?

Homework Statement Solve ln(2x+1)=2-ln(x) for x. Homework Equations The Attempt at a Solution e^(ln(2x+1)) = e^((2-ln(x)) 2x + 1 = e^(2/x) 2x^2 + x = e^2 2x^2+x-e^2 = 0 At this point, I know you're supposed to use the quadratic equation. But, my problem is with how...

[SOLVED] Logarithmic plots... Homework Statement use logarithmic plots to test exponential and power law variations This statement appears in the Cambridge A'Level Syllabus Can somebody please explain what does this statement require from the student? Helpful links would be highly...

Homework Statement solve x. Log(35-x^3)/Log(5-x)=3 Homework Equations Log(a/b)=Log a - Log b The Attempt at a Solution The answers would be 3 or 2 (so I'm guessing it has sumthing to do with quadratics) i tried to expand the left side first, then rearrange it to Log(7/x^4)=3...

Homework Statement if g(t)=(10^t)(log...t) then evaluate g'(10) ......10 <---------(my attempt at a log base 10) Homework Equations im completely lost...i don't know if i should take the ln of both sides...or what to do really. The Attempt at a Solution

Find f. (x>0) f''(x) = x^(-2) x > 0 f(1) = 0 f(8) = 0 Alright, everything was fine until one point...okay. First derivative: f''(x)=x^{-2} f'(x)=-x^{-1}+C Now here's where I'm not sure: in the next step, it will be x raised to zero, which is one. times 1/0, which is zero...

Homework Statement Given some dispersion relation for the tight binding approximation in 2D: e(k_x,k_y) = -2t_1[cos(k_x*a)+cos(k_y*a)]-4t_2[cos(k_x*a)cos(k_y*a)] Show that the density of states has a logarithmic singularity for some choice of parameters t_i. Homework Equations g(e)de=g...

Find y' if y= ln( x^2 + y^2) I thought this was just a regular natural log derivative combined with the chain rule. So what I got was (2x + 2y)/ (x^2 + y^2) But this wasn't the correct answer. So could someone help point out my mistake. Thank you.