Questions related to real and complex logarithms.

learn more… | top users | synonyms

-5
votes
1answer
59 views

Proof that $0^0 \neq 1$ [closed]

Suppose that $t = \sqrt{t}^{\sqrt{t}}$, then, it follows that; $$ t^{\sqrt{t}} = \sqrt{t}^{t} \\ \frac{1}{2}t\ln{\left(t\right)} = \sqrt{t}\ln{\left(t\right)} \\ \ln{\left(t\right)}\left[\frac{1}{2}t ...
-1
votes
2answers
45 views
0
votes
2answers
33 views

How to simplify the expression $(\log_9 2 + \log_9 4)\log_2 (3)$

Our test asked to simplify $(\log_9 2 + \log_9 4)\log_2 (3)$. I simplified the first parenthesis to be $\log_9 (8)$. So, now I have $\log_9 (8) \cdot \log_2 (3)$ and I can change to base $10$ and ...
0
votes
1answer
26 views

basic math problem relating to log thought my answer is not matching with the alternative

$1/2 \log c = 0.915$. Calculate $c$. It is a basic math problem but my answers are not matching with the alternatives. $1/2 \log c= c^{1/2}$ $ c^{1/2}= 0.915$ $c = 0.915 \times 0.915=0.83448$ ...
1
vote
1answer
13 views

Verify whether or not expression is true or not for z>0

I need to verify whether or not the below expression is true or not for $z>0$. I'm trying to understand the rules of logarithms but I can't figure out how to apply it myself or where to even begin. ...
1
vote
2answers
53 views

Solution of $5^{\log x}+5x^{\log 5}=3$

Solve for $x$ $$5^{\log x}+5x^{\log 5}=3$$ where base of log is $a$, $a>0$ and $a \neq1$ Could someone hint as how to initiate this question? I am not having any idea as how to proceed.
2
votes
1answer
71 views

How to prove $({\log_2 x})^{n+1} \le x^n$

I want to show that $({\log_2 x})^{n+1} \le x^n$ when $n \ge 1$ and $x \ge 1$. I know that ${\log_2 x}$ can be shown to be $\lt x$ with: $x \lt 2^x$ $\log_2 x \lt x$ and obviously adding the same ...
1
vote
1answer
28 views

How are floating-point numbers logarithmically distributed?

From what I remember from a lecture I had of a course I'm attending called "introduction to computational science", floating-point numbers are distributed logarithmically. What does it mean? And how ...
1
vote
2answers
84 views

How to solve the equation $x \log \log x = n$

I would like to solve the equation $x \log\log x = n$. I've seen a lot of post about the equation $x \log x$ but here I have a composition of $\log$. How can I solve it ? Thank you very much.
1
vote
0answers
28 views

Nested logarithms to represent real intervals.

Out of curiosity from this question regarding writing real numbers as an iterated sum/difference of square roots I started experimenting with another family of functions: $$\log[ \exp[1] \pm ...
11
votes
2answers
178 views

What is $\int_0^1 \ln (1-x) \ln \left(\ln \left(\frac{1}{x}\right)\right) \, dx$?

There are well-known closed-form evaluations for integrals of the form $\int_0^1 a(x) \ln \left(\ln \left(\frac{1}{x}\right)\right) \, dx $ for certain algebraic functions $a(x)$. For example, an ...
0
votes
1answer
33 views

When will the population of a sample double (using dif-eq)?

I have the initial equation $$\frac{dP}{dt}=kp$$ where P is the population, t is time, and k is some positive constant. The rest of what I'm given is that P(0) = A, what is the time for the population ...
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
18 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
27 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
16 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
53 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
44 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
48 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
43 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
24 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 ...
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
22 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
24 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
13 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}) ...
3
votes
1answer
76 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
28 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
votes
2answers
14 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?
0
votes
2answers
71 views

$\log^2n$, $\log n^2$, $\log \log n$, $(\log n)^2$; What are the differences? [closed]

What is the difference between the following: $\log^2n$, $\log n^2$, $\log \log n$, $(\log n)^2$
3
votes
6answers
120 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
26 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
68 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
70 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
28 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
68 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: ...
3
votes
2answers
98 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
24 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
37 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
32 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
35 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 ...
5
votes
2answers
116 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
30 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 ...