Logarithm Definition and 335 Threads

I'm not entirely sure if my reasoning is correct here... "[G]ive the order of each of the zeroes of the given function. 6. ##Log(1 - z)##, ##|z| < 1##" (Complex Variables, 2nd edition by Stephen D. Fisher; pg. 133) The complex logarithm function is defined in the following manner: ##log(z) =...

Let $$f(x) = k\ log_2 x$$ (a) Given that $$f^{-1}(1)=8$$, find the value of $$k$$ to get $$f^{-1}(x)$$ exchange $$x$$ and $$y$$ $$x=log_2 y^k$$ then convert to exponential form $$2^x=y^k $$ then $$2^{\frac{x}{k}} = y$$ so for $$f^{-1}(1) = 2^{\frac{1}{k}}= 8=2^3$$ then...

I came up with the following integral $$I(t,a) = \int^t_0 \frac{\log( x^2+a^2)}{1+x}\, dx $$ http://www.mathhelpboards.com/f28/fractional-logarithm-integral-5457-new/we have an attempt to solve the integral succeeded by chisigma for the particular case $$I(1,1)$$ , I don't now whether there...

Prove the following $$\int_{0}^{1}\frac{\log(1+x^{2})}{1+x}dx=\frac{3}{4}\log^{2}(2)-\frac{{\pi}^{2}}{48} $$ Good luck with this one ... :)

Here is a fun exercise to prove $$\int^1_0 \frac{\log(t) \log(1-t)}{t} \, dt = \zeta(3)$$

Here is an integral that I seen in another forum $$\int^1_0 \frac{\log(x)\log(x+1)}{1-x} \approx -0.5 $$ That was a value return by W|A . This thread will be dedicated to try to solve the integral . Any ideas will always be welcomed . The integral might require some dilogarithm identities ...

Recently in the 'Challenge Forum' the following integral has been proposed... $$\int_{0}^{\infty} \frac{\ln x}{x^{2}+ a^{2}}\ d x\ (1)$$ Scope of this note is to illustrate a general procedure to engage integrals like (1) in elementary way, i.e. without use comnplex analysis tecniques. The...

Find the following integral : $$\int^{\infty}_{0} \frac{\ln(x) }{x^2+a^2}\,dx$$

I quote an unsolved question from Yahoo! Answers I have given a link to the topic there so the OP can see my complete response.

Homework Statement Find f'(x): (abs(((x^2)*((3x+2) ^(1/3)))/((2x-3)^3)) <- Not sure why it''s not showing up but the 1/3 is an exponent to just the (3x+2).Homework Equations Product Rule and Quotient Rule for DifferentiatingThe Attempt at a Solution So I thought I should split it into two...

I need some advice, What could it possibly mean, in an article I am studying, where the results of a test (visual-spatial working memory) in relation to a variable (Maths skills in kids) is being discussed as follows: "The distribution of the variable was so negatively skewed, that it was...

I feel so dumb. I cannot figure out this relationship for the life of me.pH= -log[H+] Imagine 2 concentrations. If the hydronium ([H+]) concentration differs by a factor of 2, it means the pH of the 2 solutions differs by -log √2 HOW?! So basically, what they're saying is (logx)(log√2)=log2x...

If log[a]x=5 and log[a]y=8, solve: log[a]((ax2)/(√y))-2 --------- I am completely lost. I've tried some ways of doing this question but I can't get past the second and third steps. This is one of the last questions in my homework and I do not have a step-by-step solutions manual, only the...

A paper I'm reading states the that: for positive hermitian matrices A and B, the Taylor expansion of \log(A+tB) at t=0 is \log(A+tB)=\log(A) + t\int_0^\infty \frac{1}{B+zI}A \frac{1}{B+zI} dz + \mathcal{O}(t^2). However, there is no source or proof given, and I cannot seem to find a...

Hi, Friends. Please suggest me any link from where I can download logarithm and antilogarithm table in excel sheet or PDF file. Please help me. Thank you all

What is twice the base of the natural logarithm?

Homework Statement I've been puzzling with this for 1 hour and can't figure it out. How do you calculate the unknown x from this equation? Homework Equations ln(1-x)-5x+7.5=0

Hello, I was playing around with DeMoivre's formula ei*pi = -1 and there is something I don't quite understand about taking the natural logarithm of a certain expression. I though that e2i*pi = 1 ln[e2i*pi] = ln (1), but this yields to an imposibility 2i*pi = 0. So...

Solve the following equation for x 16-12ln(7x)=47 I know I need to isolate x . however I am unsure how to get ln(7x) separated. what i have so far ln(7x)=-31/12

Having an issue with applying logarithm rules. I'm trying to find the value of an exponent in an equation of the form: A=B\frac{(1+x)^n-1}{x} I have reviewed logarithm rules and cannot get to the answer, n, which is the only unkown variable in the equation. I've divided A by B, but am stuck at...

Homework Statement What value of x satisfies the equation: 6 \cdot e2x = 4x The Attempt at a Solution If I'm not mistaken, I can move the 6 to the superscripted part of e, resulting in: e12x = 4x And then I can take the natural log of both sides, resulting in: 12x = ln(4x) Assuming I...

Homework Statement 3 - 3^(x+1) < 5^x - 15^x 3(1-3^x) < 5^x(1-3^x) Do I have to impose 1-3^x > 0 ? It results x<0 and x>log(5,3) but book has written 0 < x < log(5,3) where did I wrong ?

Homework Statement 3x + 3x+1 = 4x Can I do this ? Log 3x + Log 3x+1 = Log4x thanks

Homework Statement Find a branch of log(z − 1) that is analytic inside the unit circle. What is the value of this branch at z = 0? 2. The attempt at a solution Alright so clearly the log(z) function is analytic at all points accept for the negative real axis. So log(z-1) will be...

Homework Statement Ok, basically I need to show that Ʃ 1/n (between 1 and n) (which is harmonic number) is θ (big theta) of ln(n), which means that is it bounded below and above by this function(upper and lower bound). But I don't quite understand how to prove it.Homework Equations I know...

Homework Statement The problem asks to solve for x log(x)=-4x+5 (the log has base 10 - not natural log) Homework Equations The Attempt at a Solution log(x)=-4x+5 10^-4x+5=x log(10^-4x+5)=log(x) -4x+5*log(10)=log(x) -4x+5=log(x) seems at first to be a simple enough...

Hello! I was trying to look for a possible expansion of the ln function. The problem is, that there is no expansion that can be used in all points (like there is for e, sine, cosine, etc..) Why do you think that is? To clarify: Let's say i do the MacLaurin expansion of ln(x+1)...

Homework Statement What is the inverse of this logarithm equation? y=-log5(-x) i tried it and i got y=-5(-x)hm.. you know how people say that if you want to find the inverse graph of something just switch the x and y coordinates from the table of values? Well i also tried that approach and...

Homework Statement How long does it take for a sum of money to double if it is invested at 8% compounded semi-annually? Homework Equations A = P(1+i)n A: Compounded amount P: Initial amount i: Interest rate n: Period The Attempt at a Solution A = P(1+i)n (2x) = (x)[1+(0.08)]2n (2n because...

Homework Statement Find all possible pairs of integers a and n such that: log(1/n)(√(a+√(15)) - √(a -√(15)))=-1/2 (that's log to the base (1/n)) The Attempt at a Solution (1/n)^-1/2 = (√(a+√(15)) - √(a -√(15)) ∴ n^4 = (a+√(15) - (a -√(15) - 2√((a+√15)(a -√(15)) ∴ n^4 = =2√(15)...

Homework Statement "If log3m = n, then determine log3m4, in terms of n." 2. The attempt at a solution I'm pretty much clueless as how to set up the equation, and what 'in terms of n' means. My guess is log3m = log3m4, but I'm confused about what to do next. The answer in the textbook...

Homework Statement Find x that satisfies: log11 (x3 + x2 - 20x) = log5 (x3 + x2 - 20x) Homework Equations logarithm The Attempt at a Solution x3 + x2 - 20x = 1 x3 + x2 - 20x - 1 = 0 Then stuck...

Homework Statement log3(3x-5) + log(1/3) 12 = 1 - x Homework Equations logarithm exponential The Attempt at a Solution The best I can get is: \frac{3x-5}{12}=3^{1-x} Can this be solved?? Thanks

Homework Statement i.2(lgx)^2 - lgx = 0 and ii. lg(2x-2)^2= 4lg(1-x) and iii. lgx-6 / lgx-4 = lgx. I simply do not manage to solve these equations, and I would therefore be happy for all help. Thanks in advance.

How do you take the log of a 2x2 matrix in general where all entries are non-zero

Homework Statement \left(ln\stackrel{2}{}(1+x)=4\right) I've never seen a number above the ln like that, usually it's on another term or simply ln(2). What does that numer mean? Is it Log(e)^2 i.e. (Loge)(Loge)? That doesn't make any sense to me. Homework Equations - The Attempt at a...

Hello, The definition is ln(x) = \int_1^x\frac{1}{t}dt I have read several sources regarding this, but what I can't seem to find is why it was defined this way. What is the justification for defining it this way, and how was ln (x) found to be the same as the that particular integral?

Homework Statement 2log(x-3)^2=log(x-3)+3Homework Equations x>3The Attempt at a Solution 2log(x^2-6x+9)-log(x-3)=3 log(x-3)=3 Not sure where to go from here seeing that it factores and becomes x=3 which makes the solution undefined

Homework Statement Differentiate x=e^{-x} The attempt at a solution \ln{x}=\ln{e^{-x}} \ln{x}=-x \frac{d}{dx}\left(\ln{x}\right)=\frac{d}{dx}\left(-x\right) \frac{1}{x}=-1 The correct answer is 1+e^{-x}. I know how to solve it that way; however, why is the above method wrong? I know there are...

What isthe use of logarithm? What i mean was what is the use of logarithm in our daily lifes and can u provide me some examples with little calculations through it?? Anyway,i just registered here :) Harris

Playing around with logarithms I found an interesting property that "log b^n(a^n) = log b(a)". Then I tried to find some kind of proof that this is right and not only a coincidence. Ι made a gereral formula for any value of both n's (α and β) so that "log b^β(a^α) = x". Therefore "a^α = b^(β*x)"...

x*log(x)=0.1*x^2

Homework Statement Evaluate without a calculator: (log34 + log29)2 - (log34 - log29)2Homework Equations The Attempt at a Solution (log34 + log29)2 - (log34 - log29)2 (2log32 + 2log23)2 - (2log32 - 2log23)2 And now I'm stuck...

Hello everybody ! I was just doing a small exercice on integration : Study the convergence of this integral : $$\displaystyle \int_{\frac{2}{\pi}}^{+\infty} \ln(\cos \frac{1}{t})dt$$ So. Ok, the study in \( +\infty \) does not cause me much trouble, it is the others which seems much...

How to solve log10000000 base is 10.

How to solve log100000000, base is 10.

If I have a convolution of two variables, say x * y, and I take the natural logarithm of this operation, ln(x*y), do the same properties of logarithms apply? So, does ln(x*y) = ln(x)+ln(y) ?

Homework Statement Hi, teachers I have been doing some work but I am confused. Have you ever heard of this great math website www.wolframalpha.com (Google for maths). This is one questions I done differantiate 3e^-4tsin(5t) and here is the link for the answers from...

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.