Logarithm Definition and 339 Threads

Homework Statement Define an analytic branch f(z) of w, such that f(z)=0 for the limit of z->\infty Now what is f(1)? Homework Equations w=\frac{z+i}{z-i} The Attempt at a Solution The branch cut of the logarithm is: (-\infty,0) All branches of the logarithm are...

(-1/2)log2 + (1/2)log1 + (3/2)log4 - (3/2)log4 - (3/2)log3 = (1/2)log[(4^3)/(2x3^3)] The above is from a textbook. Could anyone please show me the intermediate steps between the two lines? Thank you.

Homework Statement Given 3log5 xy2 + log5x = 4+2log5y, prove xy = 5. Homework Equations The Attempt at a Solution Can i prove like this? Or i must use 3log5 xy2 + log5x = 4+2log5y to prove xy=5? Meaning my final result must be xy = 5? Please enlighten me..

Homework Statement If \tilde{G_n}(\theta,\lambda)= \sum_{k=1}^{n} \tilde{g_(k,1)}(i\lambda)\frac\{{theta}^{k}}{k!}, show that...

Hello, I am having difficulty matching one term in my Laurent series to that which mathematica tells me is the correct answer. For the function f(z)=log\frac{1+z}{1-z} we know that there exists a k such that Log|1+z|-Log|1-z|+i2\pi k Now, we know that the Taylor series of f is as...

Edit: I answered my own question, I guess this thread serves no purpose so mods, you can delete this. y = x^2 ln y = ln x^2 ln y = 2 ln x Can we do the same thing with: y = x^{2/x} ln y = ln x^{2/x} ln y = \frac{2}{x} x Would that be correct? I just want to make sure because I used this...

Homework Statement The relationship between arctanh and log is: arctanh(x)=\frac{1}{2}log(\frac{1+x}{1-x}) but if i take x=1.5, I have: arctanh(1.5)=0.8047 + 1.5708i and \frac{1}{2}log(\frac{1+1.5}{1-1.5})=0.8047 + 1.5708i as expected, but using the laws of logarithm, why does this...

Homework Statement by substituting y = log2x solve for x in the following equation: √log2x = logs2√x Homework Equations logab=c then a^c = b The Attempt at a Solution if y = log2x then the equation becomes √y = log2 x^1/2 this implies √y = 1/2 log2x which simplifies to √y = 1/2 y...

Homework Statement i have some data and i have to find out if they can be put in the function f(x)=a^x or f(x)=x^a it is about how much time there goes before the population soemwhere grows or such. Homework Equations data: it is about the growth or a population in a villlage (way hard to...

Homework Statement Show that \frac{1}{x} \ln \frac{x+1}{x-1} = \sum_0^\infty \frac{2x^{2n}}{2n+1}. 2. The attempt at a solution I tried to use the relation \frac{1}{1+x} = \frac{d}{dx}\ln (1+x) and expand as a geometric series, but this did not lead anywhere since I then ended...

If I have log a b = c, what is the term for the value b? I know that a is the base and c is the exponent, but I can't think of what b is called! While I am at it, in ab = c, what exactly is c called? The power? Would that make b from the previous example the power as well? I have a...

Homework Statement Consider a branch of \log{z} analytic in the domain created with the branch cut x=−y, x≥0. If, for this branch, \log{1}=-2\pi i, find the following. \log⁡{(\sqrt{3}+i)} Homework Equations \log{z} = \ln{r} + i(\theta + 2k\pi) The Attempt at a Solution This one...

We began learn flowcharts at school. First homework is make logarithm flowchart. I don't know how work logarithm cause we didn't learn in math yet. I tried make flowchart myself but I'm sure it's wrong cause don't know how logarithm works. Can someone help me? Thanks

Hello, was wondering if anyone could please help me with the following questions as for math I have been given a substitute teacher who is of little help. Any help would be much appreciated, even if its just pointing me in the right direction Equation 1: Log (x-3) = 1 + Log 4 - Log x...

Hello I am currently studying Math B in high school and am having an extremely hard time with my current assessment. If anyone could please help me with the equations listed below it would be very much appreciated as my current Math teacher is on long service leave, and our substitute is...

Homework Statement is ln(x)3 the same as saying [ln(x)]3? Also, if there is a difference, which one applies to the exponent being moved into the front of the logarithm as in 3ln(x)? Homework Equations natural logarithms The Attempt at a Solution I just got tripped up on the...

Homework Statement The equation (attached as image) has (a)one irrational solution (b)no prime solution (c)two real solutions (d)one integral solution i would like to get help on how to find the possible values of x Homework Equations ( the equation is attached...

Homework Statement Write the quantity using sums and differences of simpler logarithmic expressions. Express the answer so that logarithms of products, quotients, and powers do not appear. log_{10}\frac{3}{\sqrt{1+x}} Homework Equations The Attempt at a Solution The...

Homework Statement 2^{5x}=3^x(5^{x+3}) Homework Equations The Attempt at a Solution ln2^{5x}=ln3^x(ln5^{x+3}) 5xln2=xln3(x+3)ln5 Here's where I get stuck... I've tried a bunch of different manipulation, but can't seem to isolate x... Thanks in advance!

Homework Statement y = 2^(sin x) Find derivative. Homework Equations The Attempt at a Solution y = 2^{sin x} ln y = ln (2^{sin x}) ln y = sin x ln(2) y' = [ln(2)] (cos x) (2^{sin x}) Yet, according to some rule in the book: a^x derivative is ln a times a^x, or in...

I have a strange problem. Have this example. log(x-2)+log(x+1)=0 Domain of these functions are: x>2, x>-1 resulting in x>2; by logarithm rule we can combine these 2 logarithms and make one logarithm. log(x-2)(x+1)=0 (-infinity,-1) U (2,+infinity) But the domain of this...

This is not a homework question. I just try it for enjoyment. Let L = log to the base x of (yz) M = log to the base y of (xz) and N = log to the base z of (xy) This is how I do it without much luck. I put all the equations in exponential form yz = x^L xz = y^M xy...

Homework Statement Write the expression as a logarithm of a single quantity 3log2-1/3log(x²-1) Homework Equations none The Attempt at a Solution 3log2-1/3log[(x+1)(x-1)]

Homework Statement Write the expression as a logarithm of a single quantity 3log5^a+4log5^b-2log5^c Homework Equations none The Attempt at a Solution ??

Homework Statement 10^-10log3 Homework Equations The Attempt at a Solution (3)10^-10log

Homework Statement log2(x3)-3= 2log2x Homework Equations NoneThe Attempt at a Solution Do I start by expanding the x to the power 3 to the log which then makes it 3log2x? or am I totally off track? Any help is greatly appreciated. Thanks

Homework Statement Find the integral of: [a*ln(b/(b -cx)) - kx] dx Where all a,b,c,k are constants and x is the variable. Homework Equations The Attempt at a Solution Rewrote is: a*INT(ln(b/(b-cx)) dx) - k*INT(x dx) I don't know how to solve the first part, (the second...

I got this question and I know a bit on how to start it, but not sure which direction is best: By considering the power series 1/(1 + x) and 1/(1 - x) show that: so I do the differentiation - ln(1 + x) = x0 du/1 + u = x - x2/2 + x3/3 - x4/4 ... which equals - = sigma (upper infinity and...

Simplify 3 log[5] (5^2) By the way ... to enter logb(x) for some base b one types: log[b](x) ... but once you've simplified the given expression you won't need to know that! 3log[5] (5^2) = (3log(5))/(log(5)) therefore: 3 log[5] (5^2) = 6 Although, would i keep the...

Homework Statement Prove that the following is true: n \Sigma lg k = \Theta (n lgn) k=1 Homework Equations the lg in this case is base 2 The Attempt at a Solution i don't kno how to apply geometric or arithmetic progression to the 1st part i was trying to substitute for k but that wasnt...

Homework Statement The question is located here http://i51.tinypic.com/2cge9mt.jpg Homework Equations My a value is -3 my b value is -3sqrt(2) my c value is -2.4 The Attempt at a Solution 1) ln(-3 - 3 sqrt(2) i) = Ln |-3 - 3 sqrt(2) i| + i arg(-3 - 3 sqrt(2) i) = ln...

Homework Statement If log4 N=p and log12 N=q, show that log3 48= Homework Equations The Attempt at a Solution I tried by substituting p and q into but i couldn't get the required answer. Can anyone help?

I am not very good in logs i have tried to attempt below problem in vain..give me an insight. Prove Log(√27 + Log √8 - Log √125 ) / (Log 6 – Log 5) =3/2 I am not good in logarithms how do you show this… This is how I did it:, Log ( ( 3√3 *2√2 ) / 5√5 ) ) / ( 6/5) ((3√(3...

Homework Statement find -Ln(1-e(i\theta) (in terms of theta) (this is me just skipping the part of the problem I know and going straight to what I can't figure out) Homework Equations ln(z) = ln(rei\theta)=Ln(r) + ln(ei\theta) = Ln(r) + i\theta The Attempt at a Solution I don't really...

May I ask how to find the E\left(ln x\right) and Var\left(ln x)? The X_{i} are random sample from the f\left(x; \theta\right) = \theta x^{\theta - 1}I_{\left(0, 1\right)}\left(x\right) where \theta > 0. I need the information in finally solving the Cramer-Rao lower bound for the variance of...

Why is there a logarithm in the entropy formula? Why is it S=kln(N) where k is the Boltzmann constant and N is the number of microstates? Why isn't it S=N?

the value same which maximizes the logarithm of the function and the plain form of the function why?? please help me, thanks

I've been asked to express the inverse hyperbolic secant function arcsech in terms of the natural logarithm and am unsure as to where to begin in solving such a problem? could someone please point me in the right direction?

How do I start to evaluate this integral? \int\frac{1}{\ln x}-\frac{1}{(\ln x)^2} dx I tried subbing u=\ln x but I'm getting no where... The answer is [tex]\frac{x}{\ln x}+C[/itex] If I differentiate the answer, I get the integral easily, but the reverse... I'm having trouble figuring out...

Homework Statement y = log base 3 e^2x Homework Equations The Attempt at a Solution I got y' = 2e^2x divided by e^2xln3 is this right? Sorry for the pathetic way of presenting this. I haven't been able to use the lancet program for proper ways to write mathematical stuff

Homework Statement y=ae^x Homework Equations rearrange to find a The Attempt at a Solution y/a=e^x x=ln(y/a) x=lny-lna lny-x=lna now how do I rearrange/inverse to seclude a

How do you differentiate : 2^n/2? You can't you just use the power rule? The correct answer is 2^n/2 (In^2) 1/2 lg^2 x n Where lg is log base 2. The correct answer is 2lgn 1/n^2 . 1/n Why is this so? Isn't lg^2 = 1? And differentiate n and we get 1? Sorry if I sound...

Homework Statement Simplify x^(3logx2 - logx5) to find an exact numerical value. Homework Equations The Attempt at a Solution 3logx2=logx2^3 or logx8, (logx8 - logx5)=logx8/5 the inverse would be x^y=8/5 (y is unknown) therefore logx8/5=y and x^(logx8/5)=x^y=8/5 and the...

I'm very new to logarithm. I've got homework to solve a ques using logarithm i.e multipication of 9356 by 0.396. And I've done it in following manner 9356*0.396 =log 9356 + log 0.396 =3.9711-1.4023 =2.5688 I know I've done it in a wrong manner as the ans is wrong. I'm very new to it. I...

Homework Statement If X is a random variable with density function: f(x) = \lambdae^{-x \lambda}where X>=0.Homework Equations Why is the expected value of X, or E[X] = \frac{1}{\lambda}?The Attempt at a Solution E[X] = \int x*(\lambdae^{- \lambda}^{x}) dx, where the integral is from 0 to...

Homework Statement Prove: \sum_{i=1}^{\infty}\sum_{j=1}^{i-1} \frac{(-1)^i}{i j}=\frac{1}{2}\ln^2 2 Homework Equations \ln 2 = \sum_{i=1}^{\infty} \frac{(-1)^{i+1}}{i} The Attempt at a Solution I'm trying to manipulate the l.h.s. of the problem to transform it into...

Homework Statement I need to prove that the following limit holds when \sqrt{s}>>m \log\left(\frac{\sqrt{s}+\sqrt{s-4m^2}}{\sqrt{s}-\sqrt{s-4m^2}}\right) \rightarrow \log\left(\frac{s}{m^2}\right) The Attempt at a Solution I've tried several manipulations using logarithms properties but had...

If we define a function f(x) such that: f(x) = \int_{1}^x \frac{dt}{t} for x>0, so that: f(y) = \int_{1}^y \frac{dt}{t} and f(xy) = \int_{1}^{xy} \frac{dt}{t} is there a way, using just these "integral" definitions, to prove that: f(x) + f(y) = f(xy) Clearly, the function...

Homework Statement the inverse laplace transform of ln\frac{s+2}{s-5} using the inverse Laplace transform of the derivative Homework EquationsL^{-1}{\frac{d^{n}}{ds^{n}}F(S)} = (-1)^{n}t^{n}f(t) The Attempt at a Solution the integral of ln\frac{s+2}{s-5} I worked to be (s+2)ln(s+2)-(s+2)...

Homework Statement Hi all, I'm having some trouble seeing why this question isn't trivial, maybe someone can help explain what I actually need to show - shouldn't take you long! :) Suppose h:\mathbb{C} \to \mathbb{C}-\{0\} is analytic with no zeros. Show there is an analytic function...