Questions related to real and complex logarithms.

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0
votes
2answers
15 views

Solution to initial condition problem

$y=-ln(1-e^{(t+c)})$ I'm trying to find the solution to the initial condition $y(0)=-ln2$ Isolate c $0=ln(2)-ln(1-e^c)$ $0=ln({2\over1-e^c})$ $-e^c=2-1$ $e^c=-1$ $c=0$ I can't figure out ...
0
votes
0answers
24 views

Weighted logarithmic ranking

I want to have a ranking of players by percentage of shots made, weighted by the total number of shots attempted. The weighting should follow a log scale, so for example Player A has 100% accuracy, ...
0
votes
1answer
33 views

What is the argument of the logarithm operator called?

In the expression $ln(y)$, what is '$y$' called. I'm asking for a noun analogous to exponent in $x^n$, where '$n$' is called the exponent. If I'm not mistaken, '$x$' in this case is the radix, or ...
1
vote
1answer
17 views

Is it possible to clear the x using the Lambert function?

$ y = \frac{x^2}{4} - \frac{ln(x)}{2} $ Solving, I get to: $ e^{4y} = \frac{e^{x^2}}{x^2} $ But I don't know how to continue.
0
votes
1answer
46 views

Stuck solving $\ln(e^y-1)-y=t+c$ for $y$

I'm trying to solve for $y$ $\ln(e^y-1)-y=t+c$ $e^y-1=e^{(t+c+y)}$ $e^y=e^{(t+c+y)}+1$ $y=t+c+y+1$ Where am I going wrong?
0
votes
2answers
56 views

Tricky Logarithmic inequality

I have tried proving this logarithmic inequality but I did not succeed. I tried to put every term on one side, I expanded and tried to use one of the properties of logarithms but the proof does not ...
1
vote
0answers
56 views

Question about the connection between exponential and logarithmic functions

Does this make sense to anyone? What advice would you give me to clarify my reasoning and explanation? One of the really "neat" features of the exponential function: $$f(x)=e^x$$ is the fact that ...
0
votes
2answers
53 views

Lambert W function with natural log

I need to solve the next equation x: $d-x+yln[\frac{d}{x}]=b$ I inserted this into Wolfram Alpha and it returned: $x = y \Bbb{W}[\frac{e^\frac{d-b}{y}d}{y})]$ y, d, b, and x are all real, ...
0
votes
3answers
45 views

Sieve of Eratosthenes Time Complexity Clarification

I've found plenty of sources claiming that the time complexity of the prime sieving algorithm Sieve of Eratosthenes is $O(n\log(\log n))$ where $n$ is the input. However, is this $\log_{10}$ or $\ln$? ...
0
votes
1answer
25 views

Is it possible to simplify $y=100x\cdot\log_{x+1} 2$ (Solved)

Is there any way to simplify the following equation, or any way to reconfigure it in a way that is possible to graph? $$y=100x\cdot \log_{x+1} 2$$
0
votes
0answers
13 views

Calculating Split Info with given equation not matching solution

I'm given the formula to calculate the Split info but cannot seem to calculate the correct answer of 0.926 that the example shows. Split Info $= -\Sigma \frac{\mid D_j\mid}{\mid D\mid} * log_2 (\frac{...
1
vote
1answer
56 views

How to solve $y= x \cdot 2^x$ for x

Can anyone help me solve this for $x$: $y= x \cdot 2^x$ I know for $y= 2^x$, that $\log_2(y) = x$ And I can get $\displaystyle \frac yx = 2^x \implies \log_2 \frac yx = x $ But I can't ...
0
votes
0answers
26 views

Resolving Zeros in Product of items in list.

Given the formula: $\sqrt [ 1/N ]{ \prod _{ n=1 }^{ N }{ { P }_{ n } } } $ where ${ P }_{ n }$ is a list of real numbers, e.g. [0.4, 0.3, 0.2, 0.1] And the ...
0
votes
1answer
24 views

Decomposition of the entropy

So, I'm reading about this property in the MacKay book. But I don't fully get it. Can someone explain it to me? There's this example: A source produces a character $x$ from the alphabet $A = \{0, ...
0
votes
2answers
47 views

Computing first k digits and last k digits of a large number using logarithm

How do we compute the first $k$ digits and last $k$ digits of a large number say $2^{N-1}$ for bigger values of $N$ using logarithms? An example for the algorithm will be greatly appreciated. I got ...
1
vote
0answers
14 views

Deformations in Variational Bayesian method

I'm studying Topic Model, but I can't understand the following transformations. $F$ is variational lower bound. $$\begin{eqnarray} F[q(z_{1:n}, \phi, \pi)] &=& \int \sum_{z_{1:n}} q(z_{1:n}) q(...
4
votes
1answer
95 views

$x+\ln(x)=0$, what is $x$?

My friend came across this strange equation and I cant find mathematical way to find $x$ without drawing $x$ and $-\ln(x)$ and see that they come across at almost $x=0.5$. Can any one help?
2
votes
1answer
30 views

Solving Weird Logarithms without a Calculator

Given "$x = \log 8$", it is very easy to rewrite the expression as "$10^x = 8$", which cannot easily be solved for by hand. However, if I plug "$x = \log 8$" into my calculator, I get "$x = 0....
0
votes
2answers
15 views

find $x$ from logarithm expression for $\log_{10}$ fraction

$$\log_{10} x = 0.5$$ I know if $\log_{10} x = 2$ then $x$ is $100$ but I don't know how to work out for a non obvious answer.
0
votes
1answer
50 views

Domain of $\ln\left(\frac{6}{6+x-x^2}-1\right)+\arcsin\left(\frac{x+1}{3}\right)$

blob:https%3A//mail.google.com/ea67134d-45a0-4cc0-9ec7-abf6d5a50852 I believe that my first condition is wrong but I don't understand why. Can somebody please help?
0
votes
2answers
39 views

Can $\ln|\cos x|$ be written as $-\ln|\sec x|$? absolute function

$\ln|\cos x| = \ln|1/\sec x| = \ln|(\sec x)^{-1}|=-\ln|\sec x|$ Is what I am doing valid? Or is it not correct because of the absolute function?
3
votes
6answers
121 views

Why isn't $-2$ solution for $x$?

I came across an logarithm problem recently. I don't know why solution to this problem cannot be $-2$. Now, don't downvote now because you don't know why I'm asking this. I know that logarithms' ...
0
votes
1answer
33 views

Argument principle and the principle branch of the complex logarithm

I've just been reading about complex analysis and came across the Cauchy argument principle. In my understanding you are taking the contour integral of $\frac{f'(z)}{f(z)}$ around a designated path. ...
2
votes
2answers
73 views

What is $\log(0/x)$?

$\log(a/b) = \log(a) - \log(b)$; Is $\log(0/x) = -\log(x)$? I watched a video claiming $\log(1/x) = -\log(x)$, which I get because $1/x = x^{-1}$ and $\log(x^y) = y(\log(x))$ but $\log(1)$... I ...
1
vote
4answers
73 views

relation betwn ln and e

If $f(x) = ln(x)$ and $f^-1(x) = e^x$ then is $e^x = 1/ln(x)$??? because I see $e^9 = 8103$ but $1/ln9 = .455$ How are they reverse? I don't understand!
0
votes
2answers
30 views

Log value to absolute

I am confused how to convert from log value to absolute value from the graph. Below is an example: In the graph, it shows the correlation of age of week and weight of placenta (in log). I can get ...
13
votes
3answers
2k views

What is the difference between the three types of logarithms? [closed]

In complex analysis I came across three types of logarithms namely $\ln$, $\log$ and $\text{Log}$. What is the difference between the three?
2
votes
1answer
71 views

How can you solve for s in this very complex problem?

I recently stumped across a problem, which I need to solve. Of course, I used an calculator and I got $s=3$, but I want to know how to do it step by step. The problem is kind of complex: $$\frac{2^{...
3
votes
2answers
101 views

Solve $\sqrt x = 1 + \ln(3 + x)$ algebraically

I am having trouble with this homework problem. I am able to graph and find the solution, but I am curious as to how one would do this algebraically. The way I began, was subtracting $1$ on both ...
0
votes
0answers
25 views

Evaluating right hand limit for a function

I want to prove the following right-hand limit (one sided limit) using $\epsilon-\delta$ definition; $\lim_{u\to 0^+} {u^{s_0} f(-ln u)} = 0$ where $f$ is a function from $R \to R$ and $s_0$ is a ...
2
votes
2answers
41 views

A limit concerning the integral of $x^n$

I pondered if the general integral of $x^n$ could be used with limits to prove that $$\int x^{-1}dx=\ln(x)+C$$ I started with $$\int x^ndx=\frac1{n+1}x^{n+1}+C$$ Then, I took the limit as $n$ ...
0
votes
3answers
48 views

How do i solve these exponential equations? [closed]

Is there a way to solve these exponential equations without using logarithms? I tried to get the same base for all the terms, but I could not make it. Is there any other general procedure that I can ...
1
vote
2answers
89 views

How to solve $3^{\sqrt{\log_{3}{x}}}+x^{\sqrt{\log_{3}{x}}}=6$

How can i solve the following equation? $$ 3^{\sqrt{\log_{3}{x}}}+x^{\sqrt{\log_{3}{x}}}=6 $$ It is clear that $x=3$ is a solution of this equation. But how can i prove that there is another solution ...
0
votes
3answers
34 views

Express $y$ in terms of $x$ in logarithmic graph

Express $y$ in terms of $x$: I know that $y = mx + c$ translates to: $\log y = n \log x + \log c$ All I can see in the question 2a of the graph below. I can tell that from the graph in question ...
1
vote
3answers
36 views

Let $x=\frac{1}{3}$ or $x=-15$ satisfies the equation,$\log_8(kx^2+wx+f)=2.$

Let $x=\frac{1}{3}$ or $x=-15$ satisfies the equation,$\log_8(kx^2+wx+f)=2.$If $k,w,f$ are relatively prime positive integers,then find the value of $k+w+f.$ The given equation is $\log_8(kx^2+wx+f)...
5
votes
2answers
118 views

Integral of the following function: [duplicate]

$$I=\int_{0}^{\dfrac\pi4}\log(\cos(x))\mathop{\mathrm{d}x}$$ I can solve it if the limit is from $0$ to $\frac\pi2$. How to do it? I have done like this, tried not to use any knowledge of series but ...
0
votes
1answer
31 views

Numerical derivative of function wrt natural log of variable (non-analytic)

The function that I am trying to evaluate is $$ \frac{d y }{d \ln(x)} $$ where $d$ is the derivative. However I have a set of data points for $x$ and $y$ with uncertainties. Now I think that this ...
4
votes
1answer
67 views

Convergence/divergence of the sum $\sum_{n=2}^\infty 1/ \ln(n!) $

Is the sum $$ \sum_{n =2}^{\infty} \frac{1}{\ln n!} $$ convergent or divergent? I have tried different methods and it doesn't work. Perhaps comparing with a divergent series will work? I'm thinking ...
0
votes
1answer
41 views

Logarithms Problem, when finding $x^n = x$

Why is it that $1^4 = 1$, when using log laws why do you get $3 = \frac {\ln1}{\ln1} = 1 \therefore 2 = 0$? I was trying to show that $(-1)^{2^x + 1} = -1$, given $x \geq 0 $ and is an integer, but ...
1
vote
2answers
57 views

Why $n^{\log_2 n}$ almost equals $2^{\log^2_2 n}$?

Just by doing some calculations: ...
3
votes
1answer
40 views

Tight lower bound for logarithm function

Is there a lower bound for the logarithm function which is tighter than, $$\log(x)\geq 1-x^{-1}$$ that works for all real values of $x>0$?
-1
votes
1answer
18 views

Prove that Log is defined on D [closed]

$D=D(0,R)$ is the disk of center $0$ and radius $R$. Given that $a>R$ and $\Phi(z)=\frac{a-z}{a+z}$, I have proved that $\forall z\in D$, $\operatorname*{Re}(\Phi(z))>0$. Prove that $f = \...
0
votes
1answer
45 views

Show that $y=e^{e^{cx}}$ is a solution of the differential equation $\frac{d^2y}{dx^2} =c^2 \cdot y \cdot \ln(y) (1+\ln(y))$

Question: Show that $y=e^{e^{cx}}$ is a solution of the differential equation $$\frac{d^2y}{dx^2} =c^2 \cdot y \cdot \ln(y) (1+\ln(y))$$ I know there are a lot of ways of solving this and I ...
0
votes
4answers
98 views

Prove $\log(n!) =\Omega(n\log(n))$ [closed]

Can someone help me prove that $\log(n!) =\Omega(n\log(n))$, that is, that there exists some positive $c$ such that, for every $n$ large enough, $\log (n!)\geqslant c\cdot n\cdot \log(n)$?
0
votes
2answers
47 views

Rules of logarithm

Can anyone help me figure out how to go from the first expression to the second? $$ \begin{equation} \ln D=u+\delta(e-p)+\gamma y-\sigma r \end{equation} $$ $$ \begin{equation} \pi \ \ln (D/Y)= \pi[...
0
votes
2answers
31 views

For what values are these logarithms true?

For what values, x and y, are both these equations true? $$\frac {\log(x)}{\log(y)} = \frac 23$$ AND $$\frac xy = \frac 23$$ How would one solve this?
1
vote
0answers
63 views

Natural Logarithm Integration

For what set of functions is $\int \frac{\ln{f(x)}}{f'(x)}\mathrm{d}x$ defined? More specifically related to the reason I ask, when $$ f(x) = \frac{c}{x} + \arcsin{x} + \sqrt{\frac{1}{x^2}-1} $$ is ...
0
votes
1answer
30 views

Solving an expression containing two added exponential functions

I have a problem solving the below equation with respect to $x$: $0.6\cdot \exp(\frac{-40}{x})+0.4 \cdot \exp(\frac{10}{x})=1$ My problem is that I have two exponential functions which are added ...
3
votes
2answers
38 views

logarithm equation with scalar on right hand side

$\log_7 (x^2-1) - \log_7 (x-1) = 2$ $\log_7 49 = 2$ => $\log_7 (x^2-1) - \log_7 (x-1) = \log_7 49$ => $\frac{(x^2-1)}{x-1} = 49$ => $x^2 -1 = 49(x -1)$ => $x^2 -1 = 49x -49$ => $x^2 - 49x + 48 = ...
2
votes
1answer
46 views

I am approximating $\ln x$ and $\log x$. How could I make these curves into a general equation?

Because I am waiting for my graphing calculator to ship, I need a quick-and-dirty way to calculate logarithms on a four-function calculator (for when I need to keep my laptop away from where I work). ...