Log Definition and 632 Threads

For instance, say I have -ln(-∞) Does the negative sign on the natural log cancel with the negative sign on the infinity? Is this true? -ln(-∞) = ln(∞) Thank you -Drc

Hi All, I'm trying to solve the following derivative with respect to the scalar parameter \sigma $$\frac{\partial}{\partial \sigma} \ln|\Sigma|,$$ where \Sigma = (\sigma^2 \Lambda_K) and \Lambda_K is the following symmetric tridiagonal K \times K matrix $$ \Lambda_{K} = \left(...

Homework Statement The initial amount of radioactive atoms on a sample of 24Na is 10^10. It's half-life corresponds to 15 hours. Give the amount of 24Na atoms that will disintegrate in 1 day.Homework Equations I started to solve it using the formula N=Initial Amount of Atoms /...

I recently struck a question that I have not been able to find an answer to. I feel like I'm missing something obvious, so I've come here for help. The derivative of a^{x} is a^{x}lna. The explanation that Stewart 5e gives is: \frac{d}{dx}a^{x} = \frac{d}{dx}e^{(lna)x} =...

The function f is continuous at some point c of its domain if the limit of f(x) as x approaches c through the domain of f exists and is equal to f(c). In mathematical notation, this is written as lim_{x\rightarrow c} f(x) = f(c) from the positive and negative sides . For ln(x) (the natural log...

Hi guys, please help me solving this =/ \[\sqrt{\log_{a}\sqrt[4]{ax}+\log_{x}\sqrt[4]{ax}}+\sqrt{\log_{a}\sqrt[4]{\frac{x}{a}}+\log_{x}\sqrt[4]{\frac{a}{x}}}=a\]

Homework Statement This is to help out a 40something calc student -- thank you all in advance for your help Homework Equations If f (y) = ln ln ln x, what is ∂y/∂x? The Attempt at a Solution I came up with 1/x, which I got by applying ∂y/∂x ln x = 1/x three times, is this...

Compute $\displaystyle\int_0^\frac{1}{2}\frac{4}{1-4t^2}dt$ Thot I could solve by using the log rule for integration namely: $\displaystyle\int\frac{u'}{u} = ln|u|+C$ for such $u=1-4t^2$ and $u'=-8t$ but then $\displaystyle\frac{1}{2}\int_0^\frac{1}{2}\frac{-8t}{1-4t^2}dt$ isn't going...

Homework Statement I have come across a rather interesting conundrum. Given the configurational potential energy partition function for a non-ideal gas: Z = Z_{internal}\frac{1}{N!}\left(\frac{2\pi m}{h^{2}\beta}\right)^{\frac{3N}{2}}(V^{N} - B_{2}(T)N^{2}V^{N-1}) where B_{2}(T) is the...

Homework Statement Solve for x logbase 4 for question 1. 1. log (x+2) - log (x-4) =1/2 log base 2: 2. log (3x+1) = 2 - log (x-1) log base 10: 3. log sq root (x^2 -21x) =1 similar just different numbers.. log (x-4) - log (x+2) =4 base 2 log (x-4)=4-log(x+2)...

My math is a little weak, so I'm having a hard time finding the elastic and plastic regions on this curve. Any further help will also be appreciated!

1)Without using tables, show that (log√125 + log √27 - √8)/ log 15 - log 2 = 3/2 What i tried was (3/2 log 5 + 3/2 log 3 - 3/2 log 2)/ log 5+log 3 - log2 then from here I don't know where to take it. 2) Find the value of x if log x2/ log a^2 = log y^4/logy I tried this...

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)...

Everything is base 10 log(ab)-2logb -1 a+b/ b2 = a/b/10 = 10a/b? But in the back of the book the answer is 10b/a...

Given that log2 3 = 1.585, find without using tables the Given that log2 3 = 1.585, find without using tables the value oflog2 ( sin ∏/3) I wrote this log2 (0.866) but was not getting the answer in the book.

Homework Statement I'd like to do a log transform on the radius variable of the heat conservation equation: qr - qr + Δr= ΔE/Δt where qr= -kA(dT/dr) My solution for this equation in cylindrical coordinates is: Tt+Δt=Tt+(Δt*k)/(ρ*c*Δr^2)* [(Tt-1-Tt)/(ln(rt/rt-1) - (Tt-Tt+1)/(ln(rt+1/rt)]...

let log_{x}y ,as a function of two variable, be defined from R^{+}_{2} to R then is it continuous at (1,1) ? if so what's the image ? here the domain is D={ (x,y)/ x ε R^{+} , y\inR^{+} }. like detailed discussion :).

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 log of 2x2 matrix [4 3] [3 4] Homework Equations e^X= A X= log A The Attempt at a Solution e^A= Ʃ (A^k)/k! then what to do?

In[48]:= 2 Log[3] === Log[3^2] Out[48]= False Why? Seems basic enough, it should find it. In[49]:= Simplify[2 Log[3]] Out[49]= Log[9] He gets it with simplify... What am I missing this time? Thank you in advance.

I found this proof on a website for the derivative of ln x: y = ln x. e^y = x, dy/dx * e^y = 1, dy/dx * x = 1, dy/dx = 1/x. My question is, why can't we use a similar method to prove the derivative of log(b)x = 1/x, like this: y = log(b) x. b^y = x, dy/dx * b^y = 1, dy/dx * x =...

Say we have 2 models: ln(y) = \beta_0 + \beta_1 x_1 + \cdots + \beta_nx_n with a known R^2 and y = \beta_0 + \beta_1 x_1 + \cdots + \beta_nx_n with a known R^2 Now I know that we can not compare the R^2's from these 2 models to determine goodness-of-fit and I am also aware of how we can...

Homework Statement Working on a computer program that will create an amortization table (a table that lists each payment on an amortizing loan). I am going to use a simple c++ array to store each row of data, and need to know the number of months required to pay off a given loan so that i...

Homework Statement Homework Equations The Attempt at a Solution I assume I can't use a calculator obviously.. so I'm quite stuck. The answer is 5, but I have no idea how to get that. (log23)(log34)(log45) ... (log3132)

Hi all, I have a summation series which goes like this, S = [log(1)]^2 + [log(2)]^2 + [log(3)]^2 + ... + [log(n)]^2 Since each term is square of the logarithm of a value, I think there are no general tricks which can be used to solve this. But is there any way to approximate the...

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.

Homework Statement Do anyone know how to solve: y=LN x y=e+1-x Homework Equations y=LN x y=e+1-x The Attempt at a Solution LN x=e+1-x x=e^e * e^1 / e^x x*e^x=e^(e+1) then I don't know how to solve, must I solve it graphically? Actually, the original question is...

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...

Hi, I'm evaluating a log, and I'm wondering how many words I can use. When I'm trying different exponents to narrow in on the exponent that I'm looking for, can I use words next to each equation? For example, "this is not big enough" next to the numbers that aren't close to the number I'm...

Hi, can I type brackets around the subscript of a log? Can I type brackets around the non subscript as well? I included what I mean in the picture below, as it's maybe easier to see what I mean. I'm just concerned that the meaning of what I wrote changes when I include the brackets. I...

what is log of z=X+JY? Thanks

Hi, I have the numbers x1, ..., xN, and I need to find the max of log2(1+xi). Is this equivalent to find Log2(1+max xi), since the Log function is monotonically increasing function of its argument? Thanks

I think this is probably the right place to put it, didn't really fit anywhere else. I've got the joyless task of writing a lab report at university and need to put a graph in it, ideally with error bars. I don't have a problem with error bars normally, but I'm coming unstuck about what to do...

Homework Statement A uniform solid cylindrical log begins rolling without slipping down a ramp that rises 28.0 above the horizontal. After it has rolled 4.20 m along the ramp, the magnitude of its linear acceleration is closest to Homework Equations The Attempt at a Solution...

Homework Statement 27x+1=32x+1The Attempt at a Solution log(27x+1)=log(32x+1) (x+1)log(27)=(2x+1)log(3) 2x+1=\frac{(x+1)log(27)}{log(3)} \frac{2x+1}{x+1}=\frac{log(27)}{log(3)} x=-2 I'm wondering how I would have continued solving this for the exact answer if \frac{log(27)}{log(3)} had...

what is the quickest way to find \sqrt[3]{n} [on a pocket calculator] whitout using any \sqrt{} or log key?

The radius of convergence of \sum\limits_{k=1}^\infty\displaystyle\frac{z^n}{n} is 1. It converges on all of the boundary \partial B(0,1) except at z=1. One way of looking at this is to analyse \sum\limits_{k=1}^\infty\displaystyle\frac{\cos n\theta}{n}+\frac{\sin n\theta}{n}. You can see the...

A Question from Em on Yahoo answers: Please can someone help with this question from a Higher Prelim paper? [A knowledge of how to change log bases is not a requirement of the syllabus.]7(a) Given that log_4(x)=P, show that log_16(x) =1/2P (b) Solve log_3(x)+log_9(x)=12

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} *...

1. Homework Statement The derivative of s(t) = (976(.835)^t - 1) +176t I have to take ln of both sides to bring the t down from the exponent. But I never had to apply ln to an equation of this complexity. Here is my attempt, but it doesn't even look close to being on the correct...

Proof d/dx [log_{b}x] = d/dx (lnx/lnb) = 1/lnb d/dx(lnx) = 1/xlnb , when x>0 I think I see the constant multiple rule at work here, but why? Is it because 1/lnb is a constant, so it is "factored" out of lnx/lnb and treated as a constant while lnx is treated as the term to be...

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...

Homework Statement there is an equation: 2^x=-6 Homework Equations The Attempt at a Solution I know that log need to be used to find x. but I can't find the log of a negative number,,

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 Find the branch points of g(z) = log(z(z+1)/(z-1)) and defining a branch of g as the principle branch of the logarithm find the location of the branch cuts. Homework Equations The Attempt at a Solution Since g(z) = log(z) + log(z+1) - log(z-1) the branch points are 0, 1...

Homework Statement Can you solve an unknown equal to some constant+log of unknown. please see attached. All the other variables are known, except Ic1. How to you solve this? Homework Equations The Attempt at a Solution I have no idea.

Hi, I'm doing this algorithm questions and i need to find the largest size n of a problem that can be solved in time t, assuming that the algorithm to solve the problem takes f(n) microseconds. For example: f(n) = log n t = 1 seconds how do i get the largest size of n in t time...