Questions related to real and complex logarithms.

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0
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5answers
63 views

Show $(\ln(x^2))^2-(\ln x)^2=3(\ln x)^2$

I read an example on integrals. I can't see how $$(\ln(x^2))^2-(\ln x)^2=3(\ln x)^2.$$
1
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0answers
35 views

Why doesn't Logz/z have zeros?

Our book claims that $\frac {Logz}{z}$ has no zeros, where Logz is the principle branch of the complex natural logarithm. However, $Logz=log|z|+iArg(z)$, correct? So $Log1=log|1|+iArg(1)=0+i0=0.$ ...
1
vote
1answer
26 views

Confused about discrete logarithm question

For purposes of explaining the notation for those unfamiliar, if we fix a prime $q$, as well as $a,b$ nonzero integers $\mod{q}$, $L_a(b) = x$ is the solution to the equation $b = a^x \mod{p}$ We are ...
2
votes
1answer
47 views

Separating the log of a sum

I know there is no formula to separate the log of a sum, e.g. $\log(X+Y)$ into two parts, but are there any approximation rules that can allow me to achieve this objective? Suppose we ignore the ...
0
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1answer
29 views

Prove this logarithm equation

I keep getting the wrong answer. Can someone please correct my working out a^x=b^(1-x) In(a)^x=In(b)^(1-x) xIn(a)=(1-x)In(b) xIn(a)=In(e)-xIn(b) xIn(a)+xIn(b)=In(e) x[In(a)+In(b)]=Ine ...
2
votes
2answers
50 views

Limit of a Logarithm with Different Bases

We are to compute $$\lim_{n->\infty}{\frac{2^{\log_3 n}}{3^{\log_2 n}}}$$ Clearly the bases are reversed between the logarithm and exponents, so I can't seem to find any logarithm or exponential ...
0
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1answer
39 views

Inverse Function of Logarithm

The answer is A but I don't understand why! $ -2 \log_e (x^2) $ can be re-written as $ -4 \log_e(x) $ right? but why do these two graphs look different? the graph $-2 \log_e (x^2) $ is one to ...
0
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1answer
14 views

Maximum value of constant in logarithm problem

The first thing I did was: make: (x-1)^2 - k > 0 (x-1)^2 > k don't know what to do after this point... the maximum value of k is 9 i dont really understand what the maximum value of k is? ...
1
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1answer
26 views

weighted average with exponential weighting

I want to create weighted average, where weights depend on value of number. If I want exponential weights is this regular? $average = \log_e(\frac{\sum_{i=1}^n e^{v_i}}{n})$ Isn't it just average of ...
1
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0answers
29 views

Interchanging from exponential form to log form

Shouldn't the answer be x = loge(everything else in the bracket) why is the loge function divided by "k" ???
2
votes
2answers
108 views

How to find $\int_2^x t/(\log t)^2 \,dt$

$$\int_2^x \frac{t}{(\log t)^2} \,dt,$$ I want to write this integral with $Li(x)$ or $Li_2(x)$. How can i do that?
1
vote
1answer
18 views

Help with integral/logarithm inequality

I have to prove the following inequality: $1/(n+1) < \int_n^{n+1} 1/t$ $dt$ $<1/n$ I thought it would be easier to attack this via integration, so I get: $1/(n+1) <$ log $(n+1)-$ ...
1
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3answers
33 views

A question on Logarithms

Q: Given that $\log_3(x) = a$ solve for $x$, $\log_3(9x) + \log_3(\frac{x^3}{81}) = 3$ \I make progress by writing $\log_3(9x) = 3^{2+a}$ and $\log_3(\frac{x^3}{81}) = 5a - 4$. However, I can't ...
2
votes
0answers
36 views

When this inequality true?

If $a$ and $b$ are non-negative integers and $c$ and $d$ are non-negative real numbers, for what values is the following inequality true? $\log((a+b)!) - \log(a!b!) \ge(a+b) \log(c+d) - (a \log(c) ...
2
votes
1answer
25 views

How to evaluate square of logarithms to solve s(n) = O(a(n))?

I've never used log before, nor worked with big-O notation, so I'm completely useless at this stuff. Any, any, any help or direction you can give would be helpful as the professor hasn't covered this ...
2
votes
2answers
69 views

Find the order of magnitude of the equation solution

Find the order of magnitude of the following equation solution: $$ x(\ln x)^{2001}=n $$
0
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1answer
17 views

clarification on logarithm problem

I was wondering if someone could explain what is going on in this problem. I understand that it makes sense that $(x = 0)$ I'm not sure why $(x<0)$ or $(x>0)$ are ruled out. LS and RS mean ...
4
votes
5answers
65 views

Calculate ln(x) using 8-digit calculator

I have a bit of a unique problem. Well, maybe not a problem because I'm really just curious about it, but... I have a simple 8 digit calculator. It has +, -, x, /, and a constant operation function. ...
3
votes
2answers
18 views

Patrial Fraction definite integral with non-real part

I have a question to find the area bounded by $y = \dfrac{x^2-4x-4}{x^2-4x-5}$ and the x-axis. First I found the bounds by solving where the numerator would equal zero. My result is $2\pm2\sqrt2$ so ...
0
votes
1answer
33 views

Relationship between logarithms and harmonic series

This article on the harmonic series says that $$\sum_{n=1}^k\,\frac{1}{n} \;=\; \ln k + \gamma + \varepsilon_k$$ where $$\varepsilon_k\sim\frac{1}{2k}$$ and this seems to generalise to ...
1
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1answer
42 views

Explicit proof of the derivative of a matrix logarithm

Firstly, I'm but a mere physicist, so please be gentle :-) I want to explicitly show that the derivative of the (natural) logaritm of a general $n \times n$ (diagonalizable) matrix $X(x)$ w.r.t. $x$ ...
1
vote
1answer
20 views

Sketching Logs with Quadratic Terms

$\log(x^2+1) = y$ asymptote at $x^2+1 > 0$ and so there is no asymptote $x$ and $y$ intercept at $(0,0)$ How do you know that the function goes both directions, and has a dip in the middle? ...
5
votes
4answers
309 views

What are logarithms?

I have heard of logarithms, and done very little research at all. From that little bit of research I found out its in algebra 2. Sadly to say, I'm going into 9th grade, but yet I'm learning ...
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1answer
16 views

Taylor Expansion and Log transformation (Time Series)

From: Time Series Analysis with Applications in R by Jonathan D. Cryer and Kung-Sik Chan. Here is the Taylor expansion: $\log Y_t = \sum_{n = 1}^{\infty} (-1)^{n+1} \frac{(Y_t - 1)^n}{n} $. How ...
5
votes
2answers
660 views

Product of logarithms, prove this identity.

Is it hard to prove this identity: $$2 \log (a) \log (b)=\log(a b)^2-\log(a)^2-\log(b)^2$$ for $a>1$ and $b>1$?
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3answers
62 views

Evaluate the integral. $\int x^2 \log(4x) dx$

The problem is $\int x^2 \log(4x) dx$ Here $\ln$ refers to the natural logarithm. So far, I know $u = x^2$ and $du = 2x (dx)$. So $dv = \ln(4x) dx$ and $v = 1/x$, but I don't know where to go from ...
3
votes
3answers
164 views

Solving ${\sqrt2}^{\,x} = {\sqrt3}^{\,x}$

I am studying logarithms and exponents. I am not sure how to go about solving this problem. I seem too keep going in circles using the rules of log and exp. $$(\sqrt{2})^x = (\sqrt{3})^x$$
0
votes
1answer
60 views

How and why does $\ln (e^{0.023t}) = 0.023t$ [closed]

How and why does $\ln (e^{0.023t}) = 0.023t$ I'm so confused.
0
votes
2answers
50 views

2 questions regarding logarithms

Sorry the tag is probably wrong but I honestly don't know what logarithm should be under. There are 2 similar questions on $\log$ that I'm unable to solve. Given that $\log_a xy^2 = p$ and ...
11
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1answer
498 views

Interesting negative decimal number notation

I was studying logarithms, and had to solve the problem: If $\log 8 = 0.90$, find $\log 0.125$. I found out the answer to be $-0.90$. That was easy. But my text book has given the answer as: ...
2
votes
1answer
46 views

Need to simplify a logarithmic expression

Can someone simplify this ($\log$ here refers to the common logarithm)? $$\sqrt{4\log2+(\log5)^2} + \sqrt{4\log5+(\log2)^2}$$ I know this has a simple solution but I cannot find it.
0
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1answer
9 views

interpretation of logarithmic in the dimension

I'm reading a paper that says "$\ Cn^{6/5}r \log n $ is not logarithmic or polylogarithmic in the dimension and one would like to know if results closer to the $\ nr \log n$ limit are possible." ...
0
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0answers
27 views

A term for function that returns a count of integer part of a real number

I have a function in JavaScript: function integerPartDigitCount(x) { return floor( log10( abs(x) ) ) + 1 } For example, ...
0
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1answer
55 views

Graphing: Given two points on a graph, find the logarithmic function that passes through both.

Is there such a method to do this? I would like to come up with a logarithmic function (a graph that looks like a square root graph) that passes through two given points. Haven't had any luck in ...
0
votes
0answers
20 views

Find the limit of the following

Log((2/n) + 2i) as n -> infinity Log(2 + (2i/n)) as n -> infinity Arg((1+i)/n) as n -> infnity (Arg(1+i))/(n) as n -> infinity for the Log questions, I am getting (i*pi)/2 + log(2) for the first ...
0
votes
0answers
33 views

Scaling a big range of small numbers to a small range of big numbers

I'm trying to make a volume meter in a Flash program. I have data coming in like: 0.008 0.0005 0.1 0.02 These numbers indicate the volume of a sound coming in ...
1
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1answer
38 views

What is the reasoning behind ways of splitting up this summation sign?

Some context: I've been studying Chebyshev's $\psi$ - function, which claims that $\psi(x) = \sum_{n \le x} \Lambda(n) = \sum_{p^k \le x} \log p$ where $p$ is prime and $\Lambda(n)$ is the von ...
0
votes
1answer
17 views

For which $z$ is the following true: $Log(iz^2) = \frac{i\pi}{2} + 2Log(z)$.

The question on our worksheet is: For which $z$ is the following true: $Log(iz^2) = \frac{i\pi}{2} + 2Log(z)$. We raised both sides by $e$ and concluded this equation holds for all $z\neq 0$, but are ...
0
votes
1answer
42 views

Logarithms with trigonometric inequality

My class is going to have an exam tomorrow, but we can't figure out how to solve such equations. $$\log_{\ \large tg(x)} \sqrt{\sin(x)^2 - 5/12} < 1 $$ We tried to transform $1$ to $\log_{\ ...
1
vote
3answers
36 views

Logarithmic equation help

$\log _5\left(x+3\right)+\log _5\left(3x-5\right)=\log _{25}\left(9x^2\right)$ I have the answer: $\left\{\frac{\sqrt{181}-1}{6}\right\}$ (only answer that falls in the domain) i understand how to ...
0
votes
0answers
22 views

Fast way to update sum of logs after each input is shifted by the same value

Suppose you have a sum of $n$ positive, increasing elements: $$\textrm{sum}_{\ 1} = \ln(x_1)+\ln(x_2)+\dots+\ln(x_n)$$ Where $x_1,\dots,x_n \in \Bbb R^+$. For a value of $C > -x_1$, where $x_1$ ...
0
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0answers
32 views

Approximation for the logarithm of a summatory

I would like to find an approximation for: $$ \log \left(\sum_{i=1}^{N} a_i\exp(-b_i^2)\exp(-c_i^2)\right) $$ with $$ a_i = \frac{1}{\sqrt{(e^2 + e_i^2)(g^2 + g_i^2)}} \\ b_i = \frac{b-d_i}{2(e^2 + ...
0
votes
1answer
33 views

Understanding math behind proof relating to binary search trees (issue with logarithms)

I am posting the entire problem starting with the initial theorem since it is pertinent to the final solution. There are two things I don't understand here. In the inductive case, why does it ...
2
votes
2answers
39 views

Solving a partial fractions

I have set up partial fractions so that$$Aln^3x-B(x+x^2)=1-x^2$$ and $$ Cln^3x+D(x+x^2)=1+x^2$$ to set up and solve the following $$\alpha(1+x)+ \gamma x= A+C$$ and from $$\frac {D lnx-B}{ln^3x} ...
0
votes
3answers
44 views

Equation in Logarithm

We have ${\log_45} = a $ ${\log_56}= b $ and we have to find ${\log_32} $. I tried the question but because of the different bases I was not able to get the solution.
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0answers
81 views

Showing that a logarithmic inequality holds

Given $0 < x_1 < x_2 < x_3 < x_4 < 1$, how can I show that the following inequality holds: $$ \frac{1}{R(x_1, x_3)}+\frac{1}{R(x_2, x_4)}<\frac{1}{R(x_1, x_2)}+\frac{1}{R(x_3, x_4)} ...
0
votes
2answers
60 views

Find Log equation from data points

I have the following data points, (left hand column goes from 0-127, right hand column goes from 30-22000 hz. Is there any calculator I can use to find a "log" function of this data, so that it comes ...
3
votes
2answers
63 views

Exponents with the same power

I've wanted to practice solving simple operations on exponents, so I've made a couple of equations to which I know the answers. $$5^x -4^x = 9$$ I feel really stupid, because I can't solve this one ...
2
votes
1answer
27 views

Logarithmic quotient

$$ \left(\frac25\right)\ln(1/2)+\left(\frac15\right)\ln(2) $$ Im having some difficulty with above quotient. Here is what i try to do. $$ \left(\frac15\right)(2\ln(1/2)+\ln(2)) $$ $$ ...
0
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1answer
68 views

Integral of Inverse of Log X

What is the value of $$\int\dfrac{1}{\log x}dx$$ I have tried many times, but failed everytime. Can anyone help me out in solving this question.