Natural log Definition and 147 Threads

when I differentiate: $$ln4x+sin(x)$$ I get: $$\frac{1}{x}+cos(x)$$ and Wolfgram agrees But then when i test this by calculating indefinite integral, I get: $$ln(x)+cos(x)$$ Which leaves me with three questions: 1. what happened to the 4? 2. why isn't it integrating back to (at least)...

Homework Statement Find the derivative of y = x^2 + x^(2x)The Attempt at a Solution By looking at the equation I think I need to use implicit differentiation + natural logs. But I can't do anything with: lny = ln(x^2 + x^(2x)) So I assume I'm wrong.. Any help??

1. how to integrate∫ (ln x)2 /x dx Homework Equations The Attempt at a Solution

Homework Statement What does it mean when the derivative of a function f(x) is in the form: d ln f(x) / d ln x ? Is it the logarithmic scale derivative, or something? Homework Equations d ln f(x) / d ln x The Attempt at a Solution Googling.

Hello, The problem is ∫(ln x)/(x + x ln x) dx. I've done most other problems in the set, but don't know where to start with this one. Although we are just learning integration by parts, I'm not sure how this would apply. I can get to ∫u/(1+u) du Thanks for any help. Homework Statement...

Homework Statement I have a problem that I'm working on that I have almost solved, yet I am just a tad off of what the book says the answer is. I will show the way I'm doing it, and where I depart from the steps the book takes. The graph of y=(x^2)^x has two horizontal tangent lines. Find...

So I've come across a derivative problem that I need to solve that is showing me some of my weaknesses in my understanding/solving of Ln and e. This is what I've done so far. \(Q = 350\frac{1}{2}^{(\frac{t}{13.1})}\) \(Q = 350 * \frac{1}{2}^{(\frac{t}{13.1})}\) \(ln{Q} = \ln{350} *...

Find the $\displaystyle\lim_{n\to\infty}\frac{2ln(2)+3ln(3)+...+nln(n)}{n^2ln(n)}$

Homework Statement Find y' of y= 1-3ln(7x)/x^4 Homework Equations The Attempt at a Solution I used the quotient rule and got: y'=x^4*d/dx(1-3ln(7x)-(1-3ln(7x)*d/dx(x^4)/(x^4)2 which is: x^4*(0-3*1/7x*7)-(1-3ln(7x))*4x^3/x^8 simplified to: 3x^4/x-1+3ln(7x)*4x^3 3x^3-4x^3+12x^3ln(7x)/x^8 take...

Determine the infinite limit. lim x->4+ ln(x^2-16) I know from graphing the equation and doing a table that the limit is -infinity, but my book is saying to do the following. Let t = x^2-16, Then as x->4+, t->0+, and lim x->4+ ln(x^2-16)=lim t->0+ ln(t) by 3

Homework Statement Solve the Equation, Check for extraneous solutions. (ln x)^2 = ln (x^2) Homework Equations -None- The Attempt at a Solution I tried simplifying it down for myself but got stuck and don't know what to do next. (ln x)^2= ln x^2 (loge x)^2 = loge x^2...

Homework Statement Use the form of the definition of the integral to evaluate the following: lim (n \rightarrow ∞) \sum^{n}_{i=1} x_{i}\cdotln(x_{i}^{2} + 1)Δx on the interval [2, 6] Homework Equations x_{i} = 2 + \frac{4}{n}i Δx = \frac{4}{n} Ʃ^{n}_{i=1}i^{2} =...

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...

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

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?

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...

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 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 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?

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!

SORRY FOR THE LACK OF FORMATTING, I SPENT 30 MINUTES TRYING TO FORMAT AND IT KEPT GETTING MESSED UP. Homework Statement Evaluate by substitution. Integral of dx/xln(x^2) Homework Equations integral of 1/u du = ln(u) + C The Attempt at a Solution u = ln(x^2) du = 2/x...

Homework Statement Evaluate the derivative of the following function: p(x) = (5x)-ln(5x) Homework Equations \frac{d}{dx}lnx = \frac{1}{x} Not sure what else... The Attempt at a Solution I know that I will have to use the chain rule in this problem, but actually...

Homework Statement Find the area under the given equation using definite integration. y = 4ln(3-x) from 0 to 2 The Attempt at a Solution Integration from 0 to 2 4 (integration from 0 to 2) (3-x) Let u = 3-x du = -dx -du = dx -4(integration from 0 to 2) du Idk where to go from there :/...

Well I've been doing fairly complex thermodynamics in classical mechanics lectures with a bit of medium to advanced class, first of all , it took me a very long time to wrap my head around the concept of Entropy, however I still don't understand why we use ln (Natural Log) to calculate the...

Homework Statement what is the integral of ln(e2x-1) dx 2. The attempt at a solution I got u= ln(e2x-1) du = 2e2x-1 \ e2x-1 du = 2 dx 1/2(integral of u du) 1/2 ln (e2x-1 ) +c = 1/4 [ln (e2x-1 )]2 + c Could you please let me know if this is correct? I don't know how to integrate ln...

Homework Statement Given the Equation ln(x+1)-ln(x)=0 find x (If it exists. Homework Equations The Attempt at a Solution ln(x+1)-ln(x)=0 ln(x+1)=ln(x) x+1 = x 1 = x-x Solution does not exist. (My book "agrees" with me in the solutions.) However, typing up the...

Homework Statement (1) Real variables x and y are related by the equation 3ln(y +4) = 2ln(x +2) − 2ln(x +9)+3ln(x^2 − 1). Determine the range of values of x and y for which the expressions on each side of this equation are defined. Find y explicitly as a function of x, that is...

Prove that sum 1/2^(n+1)*n/(n+1), from n=0 to infinity, converges to 1 - log(2), where log stands for the natural logarithm. I know that the Taylor series for log(x) about x=1 is sum (-1)^(n+1)*(x-1)^n/n, but I don't see how these two statements are consistent. Thanks for any pointers!

Homework Statement My homework problem is the double integral of y/1+xy dxdy. It is a definite double integral and both integrands have the values of a = 0 and b = 1. Homework Equations Integration by parts: uv - int(vdu) The Attempt at a Solution My first step of the double integral is I...

So I am not quite sure how to solve for x here. 1.2E-21=(.3567)(ln(x/.175))

Homework Statement Evaluate the integral when x > 0: indefinite integral of ln(x2+19x+84)dxHomework Equations I know I need to use some form of integration by parts: integral of u*dv=uv-(integral of(du*v)) The Attempt at a Solution I began by making u=ln(x2+19x+84) and dv=dx. Thus, (after...

Homework Statement ln(3x+1) = 3-lnx Homework Equations Solve for xThe Attempt at a Solution Well I put the ln on the left side ln(3x+1)+ln(x) = 3 Then I combine them ln ((3x+1)(x)) = 3 So I take e e^ln(x(3x+1)) = e^3 I get x(3x+1) = e^3 So I divide the x (3x+1)/(x) = (e^3)/(x)...

the question is simple but i can't seem to think of a solution. for what b>0 does ln(x)=b x^{2} have exactly one solution, and not 0. I've tried playing with ln rules but can't seem to think of a solution

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)

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 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...

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...

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 \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 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...

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 ??

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...

Homework Statement y and x are both close to 1. ln(y) - ln(x) \approx (y-x)(lnx)' Can someone explain me why this is true? By the way, (lnx)' is the derivative of lnx, which is just 1/x The Attempt at a Solution I guess this is something to do with the taylor series of ln(x). I tried to...

Preparing for the math test, and cannot understand what to do for one of my practice problems: I need to find if the series is convergent or divergent, using test for divergence (divergent if limit doesn't equal 0) sigma from 1 to infinity of ln((n^2+1)/(2n^2+1)) I see that I should use...

Can anybody solve for x? 6=(36/9)ln(120/x) The answer is x=22.3 I have so far got: 6=4*ln(120)-ln(x) 6=19.15-ln(x) I think it may be incorrect

Homework Statement Guys how come ln(e)=1 ? How can l prove this