Log Definition and 632 Threads

½Logb(x2-1)≈logb(x) This is an easy and useful way to calculate the log of any natural number, including primes, it won't ever give a precise result, obviously (because of the -1), but as "x2-1" will always have divisors smaller than "x", you can easily calculate the approximation by using the...

I have data (all less than 1) and I need to round down to the nearest 1/2, 1/4, 1/8, 1/16, and 1/32. I have no idea how to do this mathematically, but I'm guessing I use log or pow functions. For example: 0.81 = 0.5 or 1/2 0.33 = 0.25 or 1/4 0.18 = 0.125 or 1/8 Any help would be appreciated...

I am trying to calculate and draw a relation between (IL) and the Growth rate (m). I have used Il as range from 10^15 to 10^18 in the calculation and when I draw the relation (x-axis ) is Il and (y-axis ) is m. I converted the IL to be in log scale. I noticed unacceptable output. So, I am...

Homework Statement can we put 3log2(x)-4log(y)+log2(5) in one logarithm it try in all the ways but i can't find the solution . Homework Equations loga(b)=logx(b)/logx(a) log(b*a)=log(b)+log(a) The Attempt at a Solution log2(5x^3)-log(y^4) log2(5x^3)-log2(y^4)/log2(10)

Homework Statement Prove the following statement: ln|1+\sigma x | = \frac{1}{2} ln|1-x^2| + \frac{\sigma}{2} ln| \frac{ |1+x|}{|1-x|} Homework EquationsThe Attempt at a Solution Starting from right to left would be easier: = \frac{1}{2} ln|(1+x)(1-x)| + \frac{\sigma}{2} ln| 1+x| -...

Homework Statement A computer can perform 1010 ops/s. Assume 1 op per 1 input. Given the following algorithmic complexities how many inputs can be performed in an hour. n2 n3 100n2 n log n 2n 22n Homework EquationsThe Attempt at a Solution [/B] C = 1·1010 ops/s · 3.6·102 s/hr C = 3.6·1012...

Homework Statement Limx--> ∞ Ln(x^2-1) -Ln(2x^2+3) Homework EquationsThe Attempt at a Solution Ln(x^2-1)/(2x^2+3) Then I divided the top and bottom by x^2 so in the end I got (1/2). Is this right?

If $\{x_n\}_{n \ge 1}$ is real sequence and $\limsup\limits_{n \to \infty} \frac{1}{n} \log |x_{n+1}-x_n|<0$, prove that $\{x_n\}$ is Cauchy sequence. My work: Let $a=\limsup\limits_{n \to \infty} \frac{1}{n} \log |x_{n+1}-x_n| <0$. Then, for every $\varepsilon >0$ there exist $N \in...

hi, anyone can have the idea how to solve the log of a power series? i.e. log(1+ Σ_{j=1}^{∞}(1/z^{2 j-1}) f^{j})

First Question: Solve the following system of equations log{x+1}y=2 log{y+1}x=1/4 Work: Turned them into equations (x+1)^2=y (y+1)^(1/4)=x Substituted second equation into the first equation ((y+1)^(1/4)+1)^2=y factored out and eventually got ((y+1)^1/4)^2+2((y+1)^1/4)+1=y Tried...

We have the rational function : $$f(x)=\frac{(1+ix)^{n}-1}{(1-ix)^{n}-1}\left(\frac{1-ix}{1+ix}\right)^{n/2}\;\;\;,\;\;n\in \mathbb{Z}^{+}$$ It's not hard to prove that ...

Hey all, I've had this point of confusion for a bit and I have thought that with time I may be able to clear it out myself. Nope, hasn't happened. I think I need help. Let us say we have the following \phi_{k+1}=\phi_{k}+v_k where, v_k\overset{iid}{\sim}\mathcal{N}(0,\sigma^2) and...

I need to find the Maclaurin series of this function: $$f(x) = ln(1 - x^2)$$ I know that $ln(1 + x)$ equals $$\sum_{n = 1}^{\infty}\frac{(-1)^{n - 1} x^n}{n}$$ Or, $x - \frac{x^2}{2} + \frac{x^3}{3} ...$ If I swap in $-x^2$ for x, I get: $$-x^2 + \frac{x^4}{2} - \frac{x^5}{3} +...

I'm examining the Maclaurin series for $f(x) = ln(x + 1)$. It is fairly straightforward but there are a few details I'm not getting. So: $$ ln(x + 1) = \int_{}^{} \frac{1}{1 + x}\,dx$$ which equals: $A + x - \frac{x^2}{2}$ etc. or $A + \sum_{n = 1}^{\infty}(-1)^{n - 1}\frac{x^n}{n}$ I'm...

$\large {S6.7.1.13}$ $\tiny\text {natural log Integration}$ $$\displaystyle \int e^{\sqrt[3]{x}} \, dx = 3\left(x^\frac{2}{3} -2\sqrt[3]{x} +2\right){e}^\sqrt[3]{x}+C \\ u=x^{1/3} \therefore 3{x}^{\frac{2}{3}} du = dx $$ $\text{not sure if this is how to start to get to a 3 term answer}...

I have this integral $$\int_{}^{}\frac{1}{{2}^{lnx}} \,dx$$ I'm not sure the best way to do it. I tried u-substitution: $u = {2}^{lnx}$ and thus $u = {x}^{ln2}$, therefore $du = ln2({n}^{ln2 - 1}) dx$. However, not sure how to proceed from there.

Supposing we have $f(x) = {2}^{lnx}$, how would we find $f'(x)$?

I was talking to my professor and she said that $(ln n)^a < n$ for all values of $a$. Is this true or was I misunderstanding?

$\large{7.R.79} $ $\tiny\text{UHW 242 log integral }$ https://www.physicsforums.com/attachments/5717 $$\begin{align} \displaystyle x& = \frac{1}{u} & {u}^{2 }du&={dx } \end{align} $$ $$I=\int_{0}^{\infty} \frac {\ln\left({\frac{1}{u}}\right)} {1+\frac{1}{{u}^{2 }}} {u}^{2} \,du \\ Stuck🐮...

If I have $\ln\left({a}\right) - \ln\left({b}\right)$ that would equal $\ln\left({\frac{a}{b}}\right)$ or $-(\ln\left({b}\right) - \ln\left({a}\right))$ which is also $- \ln\left({\frac{b}{a}}\right)$. So does this mean $\ln\left({\frac{a}{b}}\right)$ equals $- \ln\left({\frac{b}{a}}\right)$?

I have this sequence: $${a}_{n} = \ln \left(\frac{12n + 2}{-9 + 4n}\right)$$ I need to find the limit of this sequence. How can I go about this? Do I need to apply L'Hopitals rule? I'm unsure how to simplify this expression. If I use the rule $\ln(\frac{a}{b}) = \ln a - \ln b$ I get $\infty -...

$\tiny\text{LCC 206 {7.r.39} Integral log }$ $$\int\frac{xe^{2x}}{\left(1+2x\right)^2 }\ dx $$ Since $2x$ is in numerator and denominator thot it might be A good candidate for $\begin{align}\displaystyle u& = 2x & du&= 2 \ d{t} \\ \end{align}$ Then...

$\tiny\text{LCC 206 {7.R.31} Integral log }$ $$\displaystyle I=\int_0^{\ln\left({10}\right)} \frac{e^{x}\sqrt{e^{x}-1}}{e^{x}+8} \ dx \\ \begin{align}\displaystyle u& = e^{x}-1 & du&= e^{x} \ d{x} \\ \end{align} \\ I=\int_0^{\ln\left({10}\right)} \frac{\sqrt{u}}{u+9} \ du $$...

Homework Statement \lim\limits_{x \to 0} \left(\ln(1+x)\right)^x Homework Equations Maclaurin series: \ln(1+x) = x - \frac{x^2}{2} + \frac{x^3}{3} + ... + (-1)^{r+1} \frac{x^r}{r} + ... The Attempt at a Solution We're considering vanishingly small x, so just taking the first term in the...

Homework Statement A cannon shoots bullets of mass m0 and velocity v0 at a massive log of wood of mass 100m0. the interval between the bullets is t0. the surface is smooth. the bullets are stuck in the wood. the penetration time of the bullets is very short, relative to t0. 1) What's the log's...

Homework Statement Two tugboats are pulling on a large log, as shown in the following diagram. The log has a mass of 250 kg and is initially at rest. How far have the tugboats moved the log after 10 s? Homework Equations c2 = a2 + b2 - 2abcosC c = (a2 + b2- 2abcosC)1/2 The Attempt at a...

Homework Statement solve the log x²-4x-5 on the base x-2.[/B] Homework Equations I read a comment from someone that also saw the question that says: The Attempt at a Solution If it was x²-4x+4, that would be igual (x-2)² and the answer would be 2, but I have no idea the guy got these...

Hi, I'm stuck on the following proof: \log[3] = \frac 1{729} \sum_{k=0}^\infty \frac 1{729^k} \left[\frac{729}{6k+1}+\frac{81}{6k+2}+\frac{81}{6k+3}+\frac 9{6k+4}+\frac 9{6k+5}+\frac 1{6k+6}\right] Manipulating and converting summands to integrals of the form $x^{-(6k+n)}$ over {x,0,3} seems...

Homework Statement (1/25)^x+3=125^x+3 Homework Equations I have used log on both sides but keep getting an incorrect answer. The Attempt at a Solution How would solve this type of equation. I set the bases both to 5, make them equal to each other and i can't get the right answer.

I was supposed to simplify the expression ##\ln |\cot {x}|+\ln |\tan {x}\cos {x}|## and apparently it’s wrong. Where’s the mistake? Is it not simplified enough or . . . ? ##\ln |\cot {x}|+\ln |\tan {x}\cos {x}|## ##=\ln |\frac {\cos {x}}{\sin {x}}|+\ln |\frac {\sin {x}}{\cos {x}}\cdot \cos...

This is a microeconomics problem that I am trying to solve. I am uncertain whether my FOCs are correct. Thank you. The objective function: ui(x1i, x2i….xLi) = Σllog[xli]; The constraint: ΣLl=1p1xl ≤ w L: Σllog[xli] + λ (w - ΣLl=1p1xl) FOCs are: L1 = 1/x1 – λ(w-p1) =0 L2 = 1/x2 – λ(w-p2)...

Homework Statement \textbf{The Logarithmic Series Distribution}. We will examine the properties of a the Logarithmic Series Distribution. We will check that is is a probability function and compute a general term for factorial moments and, hence, compute its mean and variance. This distribution...

a>b ⇒ Lim(a–b)→0 Logc(a+b) ≈ Logc(a) + Logc(√a⋅b) b>a ⇒ Lim(b–a)→0 Logc(a+b) ≈ Logc(a) + Logc(√a⋅b) a∈ℝ b∈ℝ c∈ℝ / c>0

So, I found this method, I don't think I was the first to, though, but I don't see any post related to this anywhere on the internet, so maybe there's a slim chance I was the first? Anyway, it doesn't really matter. The method does not give the precise result, only approximations, but I find it...

Homework Statement Why does a log float horizontally as opposed to vertically? Homework Equations Nah The Attempt at a Solution I can kind of imagine why a vertical log would be in unstable equilibrium, but the thought isn't quite as logically cohesive as I'm comfortable with, so could...

Hi all, I am facing the problem while executing my fortran (77) program. please help me how to fix it. As I understood, the error means that the domain of log function has included zero values or negative values...But I could not understand...In my case... there are no zero or negative...

How is it true that: Log[L+(Z^2+L^2)^(1/2)] - Log[-L+(Z^2+L^2)^(1/2)] = 2{Log[L+(Z^2+L^2)^(1/2)] - Log[Z]} ?

Homework Statement f(c,l) = log(c - ψ(1-l)^θ ) What is the derivative of this function wrt. l and c?Homework Equations I know that the derivative of log (x) = 1/x The Attempt at a Solution I got wrt c: 1/ c - ψ(1-l)θ and wrt l: θψ(1-l)^θ-1 / c - ψ(1-l)^θ

Hi folks, I'm revisiting logs for the first time in a long time through distance education and I was wondering if someone could have a look over a question I've answered and let me know if I've done it correctly or if I'm way off please Find x if Log3(10x – 1) – 2 = 2log3x I instantly divide...

So looking through my notes I can't seem to understand how to get from one step to the next. I have attached a screenshot of the 2 lines I'm very confused about. Thanks. BTW: The equations are for the log likelihood in a mixture of gaussians model EDIT: To elaborate I am particularly...

Hi all, I am currently operating a piece of equipment that essentially collects particles and separates them based on their size. Essentially you have 8 stages, and each stage has a differing size of particles it collects. For example: Stage----Size of Particles (D) (um)-----Mass Collected (M)...

Homework Statement The problem is to sketch lines of constant u and v in the image plane for the function Log[(z+1)/(z-1)]. Homework Equations z=x+iy The Attempt at a Solution In order to do this I have to get the expression into u+iv form, so that I can read off and manipulate the u and v...

In the figure it could also be possible to connect the transistor Q1 as a diode by shorting its collector with its base ..but instead it is done by keeping both base and collector at ground... The text have to say that if it would be connected the other way(i.e by shorting collector and base...

Homework Statement Hello! Binary search requires O( log2(n) ) operations in the worst case. My math doesn't add up. I would be grateful for help. Homework Equations For example: Find number 8 in the set 1234578. The Attempt at a Solution The set contains n = 7 elements. 1) take the middle...

Hi members,see attached PdF file.Have you any idea to prove thes integrals Thank you

I noticed the scan was cut off on the second image at the bottom right, but I came up with x= 31/5 My first test in Calc I begins tomorrow and I want to know that I'm headed in the right direction. I think I understand to some extent how logarithms can be expanded and condensed though I'm...

If there a finite field where both group structures have hard discrete logs? Discrete log in the additive group means multiplicative inverse.

Is ##\log \log n \times \log \log \log n = \Omega(\log n)## How can we prove it. Actually I'm trying to prove that ##f(n) = \lceil(\log \log n)\rceil !## is polynomially bounded. It means ##c_1 n^{k_1} \leq f(n) \leq c_2 n^{k_2} \quad \forall n > n_0## ##m_1 \log n \leq \log [f(n)] \leq m_2...

Hi everyone, I need some help to solve this problem: The direction states to find the value by using the log table $\log_{3}\left({825.6}\right)$ Work: I using the change of base: $\log_{3}\left({825.6}\right)=\frac{\log\left({825.6}\right)}{\log\left({3}\right)}$ I look up the values of...

Homework Statement In the figure, a 128 kg uniform log hangs by two steel wires, A and B, both of radius 1.15 mm. Initially, wire A was 2.80 m long and 2.00 mm shorter than wire B. The log is now horizontal. Young's modulus for steel is 2.00 × 1011 N/m2. What are the magnitudes of the forces...