Questions related to real and complex logarithms.

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2
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1answer
144 views

Solving for $y$ in $y = x \ln(y)$

I want to solve $y = x \ln(y)$ for $y$ in terms of $x$. Wolfram Alpha kindly produces this plot with the solution, $y = -x W(-\frac{1}{x})$, where $W$ is the Lambert function. However, that only ...
5
votes
1answer
549 views

Comparing Powers of Different Bases

How can I know if one power is bigger than the other when the bases are different? For example, considering $2^{10}$ and $10^{3}$ the former is the greater one, but how to prove this? Logarithms? ...
6
votes
1answer
123 views

logarithms power equation

I got a home work question to solve the following: $$ 27x^2 < x^{\log_3x} $$ can any one please explain how to solve this type of equation? I have no idea what to do or what to search for.
8
votes
6answers
433 views

Has anyone talked themselves into understanding Euler's identity a bit?

What does the ratio of the circumference of a circle to its diameter have to do with the base of the natural logarithm and $\sqrt{-1}$?
0
votes
2answers
116 views

How can I calculate limit of division of two logarithms

How can I calculate $\lim\limits_{n \to \infty} \frac{\log_{a} n}{\log_{b} n}$. Where $a$ and $b$ are two integers.
1
vote
0answers
74 views

lower bounds for maximum computing times for integer factorisation

Supposing that n were known to have two prime factors, and that the computer had a database of all the primes $<\sqrt{n}$. Then, unless n is square, one factor would be $<\sqrt{n}$. If an ...
0
votes
3answers
139 views

Very basic question about logarithm

I don't fully understand why you need to solve it this way... $$x^25\log(2x+1)+9(-5)\log(2x+1)=0 $$ $$(x^2-9)5\log(2x+1)=0$$
15
votes
3answers
572 views

challenging alternating infinite series involving $\ln$

I ran across an infinite series that is allegedly from a Chinese math contest. Evaluate: $\displaystyle\sum_{n=2}^{\infty}(-1)^{n}\ln\left(1-\frac{1}{n(n-1)}\right).$ I thought perhaps this ...
1
vote
1answer
159 views

Can you use a logarithm coefficient in a linear equation?

I have an equation that looks like $x+(\ln3)y+z=0$ where there's a natural logarithm as a coefficient. Is it possible to have this in a linear equation? I know that you cannot have a root or a product ...
1
vote
1answer
46 views

Find M, since $\log_5 M = 2\log_5 A - \log_5 B+2$

Find M, since $\log_5 M = 2\log_5 A - \log_5 B+2$ I tried this: The answer is in function of A and B. $\frac{\log_M M}{\log_M 5} = 2\frac{\log_M A}{\log_M 5} - \frac{\log_M B+2}{\log_M 5}$ ...
0
votes
1answer
73 views

Re-writing a logarithm to a power

Given: $$(4\ln x)^2$$ Is this simplified to $8\ln x$, (multiplying the expression by 2), $32\ln x$, (square $4$ ($16$), then $\ln x$ ($2\ln x$) and combine again), or something else? Just to be ...
4
votes
1answer
449 views

Help understanding this formula on mutual information (used in bioinformatics)

I'm a bit lost on understanding this formula in my bioinformatics text, and I appreciate any tips or advice. Mutual Information, $\operatorname{MI}(X; Y)$ is: $$ \mu = \sum_x \sum_y p(xy) ...
5
votes
3answers
257 views

Solving the equation $3^{5x-2}=8^{8x-9}$

I'm trying to solve the equation $$3^{5x-2}=8^{8x-9}.$$ I'm assuming I need to do some work with logarithms, but I don't know what to do. Thanks in advance!
3
votes
2answers
502 views

Spectral Centroid computation issue

I guess my problem is related to logarithmic <-> linear scales. I'm trying to create a colored wave form by using a Spectral centroid. So far I got the color but the scaling is incorrect. Why this ...
0
votes
2answers
91 views

Solving $7 = 8 - 2e^{-3k}$

So, this is an assignment my friend and I have for our homework: $7 = 8 - 2e^{-3k}$ And the solution should be: $\frac{1}{3\ln(2)}$ But, I have no idea how they got there. I tried doing: ...
1
vote
1answer
263 views

How do you prove the following inequality concerning complex Logarithms?

If $0<|w|<1/2$, then $2|w|/3<|\operatorname{Log}(1+w)|$ using power series and modulus inequalities.
2
votes
4answers
95 views

Show that these are equivalent $x-\ln|1+e^x| = -\ln|e^{-x}+1|$

Can anyone help me show that the following equations are equivalent? $$x-\ln|1+e^x| = -\ln|e^{-x}+1|$$ I'm having a little trouble. It should be an easy solution, where I take one equation, start ...
3
votes
1answer
166 views

Groups where discrete logarithm is hard

What are examples of groups, where DLP (discrete logarithm problem) is hard? Two obvious ones are: integers modulo $p$ ($p$ being prime) and elliptic curves over finite fields. What are the others?
1
vote
2answers
135 views

Logarithm question

Alright, I'm helping a friend, but can't seem to be able to crack this question : If $\log_3 20 = a$, $\log_3 15 = b$ then how do we represent with a,b $\log_2 360$?
2
votes
2answers
763 views

Difference between Logarithms of different bases

Every time i see a logarithmic function and if it so happens that i'am required to take the derivative or the integral of that particular function i get stumped and i tend to avoid that problem. What ...
1
vote
1answer
663 views

Extracting angular velocity tensor from orthogonal matrices

Let us suppose we have two orthogonal rotation matrices representing a three-dimensional rotations $$\mathbf{R}(t)$$ and $$\mathbf{R}(t+\Delta t)$$ How is it possible to extract the angular velocity ...
2
votes
3answers
244 views

How do I solve this equation involving a logarithm?

I'm running in circles and I don't understand how to do this. $$x\log(x) = 100$$ Where the $\log$ is in base $10$, I understand that $\log(y)=x$ is $10^x = y$. So is it the same for $x\log(x) = ...
5
votes
1answer
1k views

How does Knuth's algorithm for calculating logarithm work?

I had a look at Knuth's The Art of Computer Programming, book 1. In chapter 1, section 1.2.2, exercise 25, he presents the following algorithm for calculating logarithm: given $x\in[1,2)$, do the ...
13
votes
5answers
5k views

Calculate logarithms by hand

I'm thinking of making a table of logarithms ranging from 100-999 with 5 significant digits. By pen and paper that is. I'm doing this old school. What first came to mind was to use $\log(ab) = ...
26
votes
3answers
8k views

What algorithm is used by computers to calculate logarithms?

I would like to know how are logarithms calculated by computers. The GNU C library, for example, uses a call to the fyl2x() assembler instruction, which means that ...
5
votes
7answers
2k views

Is there any significance to the logarithm of a sum?

Many years ago, while working as a computer programmer, I tracked down a subtle bug in the software that we were using. Management had dispaired of finding the bug, but I pursued it in odd moments ...
-1
votes
2answers
859 views

Basic logarithm questions

What is the value of $5^{\log_{5} 2}$? If $m = y$, which expression is equivalent to $\log (100 m^2$)? Which base logarithm do I use? Is it self implied that its $\log_{10}$? How do I solve it? When ...
2
votes
2answers
95 views

Difference of Logarithms to form a quotient?

Write as a single logarithm: $\log_8(5) - 2\log_8(6)$ To my understanding; because they are the same base you can just evaluate $\log_8\left(\frac{\log(5)}{\log(6)}\right)$ which is shown on the ...
3
votes
0answers
248 views

Can the Baker-Campbell-Hausdorff formula for $\ln(AB)$ be simplified for similar, diagonizable matrices?

Given two similar, diagonizable square matrices $A$ and $B$ that do not commute, can the Baker-Campbell-Hausdorff formula be simplified exploiting the similarity to obtain a nice expression for ...
0
votes
1answer
600 views

Simple function for damping (programming)

I'm programming a game and am looking to create a non-linear relationship between input and output, such that as the input increases, the output increases, but the higher the input value, the ...
5
votes
4answers
242 views

Mathematical notation/name for the number of times a number can be divided by 2

I am using this simple snippet of code, variants of which I have seen in many places: for(int k = 0 ; n % 2 == 0 ; k++) n = n / 2; This code repeatedly ...
0
votes
1answer
103 views

Simple physics for a graphical user interface widget

I have developed a spinner view for an Android application. It's like the spinner wheel on the Price Is Right with Bob Barker (If you're not familiar with that show watch this video). I am looking ...
0
votes
2answers
87 views

References on Breaking Integrals into Logarithms

I've seen that (tough) integrals may be broken into answers in logarithmic form. In other words, many integrals have an alternate answer that is in the form of a function involving logarithms. An ...
2
votes
1answer
110 views

Sequence to differentiate log function

One problem I've been asked to solve is giving me some trouble on the particular sequence to solve. Find the differential of $$g(t)=\frac{10 \log_{4}t}{t}$$ Looking at the problem, you can see that ...
6
votes
3answers
2k views

Is putting absolute values around the argument of a log obtained through integration incorrect?

I've always been taught that when integrating a function of the form $f'(x)/f(x)$ to put an absolute value around the argument of the resulting logarithm. For example: $$\int\frac1{x}\mathrm dx = ...
2
votes
2answers
320 views

Understanding why this natural log formula rewrite works

I came across this question in my homework and am unsure why it works this way. Given $y= \ln(e^{x^2})$, find the derivative. The given answer work showed the formula rewritten as $y=x^{2}$ before ...
3
votes
2answers
143 views

$\frac{N\log{N}}{k\log{k}}\approx \log_{k!}{N!}$

What is the simple way to show that $$\frac{N\log{N}}{k\log{k}}\approx \log_{k!}{N!}\quad?$$ I tried to use the factorial and the log rules but.. Thanks.
2
votes
1answer
162 views

Logarithm rules

What can I do with these expression: $2^{\log _{\frac{4}{3}}n}$ and $2^{\log _{4}n}$ if I don't want to have $n$ in the exponent? I tried nothing because I didn't have any good ideas. Thanks.
2
votes
1answer
278 views

Zooming formula

I am sorry if this is a noob question, I need help with relatively simple math problem and assurance that I understand the problem correctly. I have a map-like program that zooms in and zooms out if ...
0
votes
2answers
100 views

Why do I get different results using the e function for the ln?

I have a question which Kind of makes me crazy right now. If I have the equation $1=\ln(2•3)$, I could then use the e function to remove the $\ln.$ Doing that I get $e^1 = 6.$ Now say we are using the ...
11
votes
2answers
1k views

Motivation for Napier's Logarithms

In the wikipedia article on logarithms, I am clueless about the approach and motivation for the following computations done by Napier (and the mysterious appearance of Euler's number) in this section. ...
1
vote
1answer
80 views

Solving for Exponents and Logarithms

I was discussing a small experiment with a friend of mine this week. He said, "we can just do 3 trials." I said, "sure, but the subject will have to get all 3 trials right to be better than chance." ...
0
votes
2answers
68 views

Trouble understanding how an equality is obtained

(This is from a proof by contradiction, so that's why the equality does not actually hold. Edited for brevity; I don't think I've omitted anything pertinent to my questions.) [...] The ...
1
vote
1answer
184 views

Solving an exponential equation

Alright, here's the equation: $$‎1.08^x = 1.10^{x-1}$$ I know I need to use logarithms, but I can't figure how to do it. Thanks in advance!
4
votes
2answers
303 views

Length of a number

Is there a method which would allow me to precisely calculate length of the largest number which has been created during multiplying two numbers? What I mean is this: 1258 * 2569 Multiplying the ...
1
vote
1answer
474 views

Why can't you integrate all power functions without a log function?

You need a logarithm function to solve all power functions. That's a fact. Power functions look like this: $f\colon x \mapsto a x^r \qquad a,r \in \mathbb{R}$ But why would you need a logarithm ...
4
votes
1answer
163 views

Show the correctness of a logarithmic inequality

Let $p_1>p_2$ and $n_1>n_2$ be positive numbers. I want to show that, $$ \frac{\log \left(\frac{p_1}{n_1}+1\right)}{\log \left(\frac{p_2}{n_2}+1\right)}\leq \frac{\log ...
1
vote
2answers
135 views

Stuck on a homework question: if $t = \frac{1}{x}$

If $\displaystyle t = \frac{1}{x}$ then a) Explain why $\displaystyle\lim_{x \to 0^-}f(x)$ is equivalent to $\displaystyle\lim_{t \to -\infty}f\left(\frac{1}{t}\right)$ b) Using that, ...
1
vote
2answers
97 views

Solution of equations involving logarithm and simple equation

I have two equations as below: m = c - n m = log(n) + 1 What approach should I take to solve this. I am sorry, I forgot to mention the variables here. 'c' is ...
9
votes
1answer
407 views

Is there a binary spigot algorithm for log(23) or log(89)?

The Bailey-Borwein-Plouffe formula yields a binary spigot algorithm for π, and related formulas give the bits of log(2) and those of the logarithms of some other integers. I got stuck (over a year ...