Logarithmic Definition and 355 Threads

Homework Statement Image of the problem: http://prntscr.com/addkf Homework Equations My question is how I can solve the equation I gave above. Should I use logarithmic differentiation? Because I think that the logarithmic differentiation is used when y = (the equation) but my problem is f...

Let me start by saying my understanding of logarithms is relatively limited, with that out of the way on to my question. The question I have is in a situation where you have 2 items that are inversely related and both have a starting point of 100%. How would you calculate the point where...

I have a simple geometry question hopefully I'm posting this in the right forum. I want to draw a simple logarithmic spiral using only compass and ruler or any other simple mechanical means. The requirement is that each spiral must be halfway from the center to the next spiral. Is there a...

Homework Statement Solve 3(6x-1) = 1 + 4/6x giving your answer in the form x = a - log6b where a,b are integers (Z) Homework Equations The Attempt at a Solution 3(6x)(6-1)(6x) = 6x + 4 Let 6x be y, (1/2)y2 - y - 4 = 0 y = 1 ± √(1+8) = 1 ± 3 3x = 4 xlog63 = log64 What...

We currently have a thread about logarithmic corrections to the basic black hole entropy formula. I was thinking about attempts to relate the magnitude of dark energy to the area of the cosmological horizon, and about the various analogies made between the cosmological horizon and the horizons...

Ashoke Sen has written a paper http://arxiv.org/abs/1205.0971 which uses path integrals in Euclidean gravity to compute "Logarithmic Corrections to Schwarzschild and Other Non-extremal Black Hole Entropy in Different Dimensions". Sen starts by listing several varieties of extremal black...

I was reading a book and it said the sun was 10^12 Logarithmic. What is the measurement of a Logarithmic?

Can anyone check my work? I'm doubtful of my answer. Homework Statement The bacteria in a 4-liter container double every minute. After 60 minutes the container is full. How long did it take to fill half the container? Homework Equations I used: F = A × 260 (1/2)F = A × 2x F...

Homework Statement hi i have the folowing data i would like to plot in matlab plotERRLW = 0.0466 0.0111 0.0074 0.0046 NX = 50 500 1000 2000 i am using a logarithmic graph to gain a straight line, if i wished to find the gradient of the line...

I'm a very conceptual person, and I've been reading about exponential and logarithmic growth but don't fully have the kind of conceptual grasp on the two and how they differ that I'd like, so I"m curious: What is the difference between exponential growth and logarithmic growth and what causes...

Homework Statement 4log45 Homework Equations ay = x ~~~> loga(x) = y The Attempt at a Solution I've separated the problem and decided to solve the logarithmic section first giving me: 4x = 5 I could move forward if I wasn't stumped on how to figure out what x is in this...

2n *logn =0.1 *n^2 solve for n please and thanks! pozhalste e spaciba! por favor a obrigadao

Hey guys, I was reading a brief article which described the logarithmic integral for approximating π(x) in two ways: ∫x/log(x) dx and ∫1/log(x) dx I am aware that the second is the actual definition of li(x) but the top is used extremely frequently and upon trying out the top it...

If I was interested in determining how to balance the rate of reinvestment of profits back into the original investment (to add to its compounding potential) while still growing the profit return on the investment. How would I go about calculating something like that ?

Okay, so in class I learned that: 10^log(4x) = 4x But I don't understand why. I get that a log without a subscript is considered base 10, so: 10^y = 4x Is the way to understand "log(4x)", right? What if the problem was a different base? Would the "10" coefficient and 'log' in...

Having problems with these questions, what's putting me off is for example the first question, if the numbers 9 and 5 were the same I think I could do it. Do I have to get them to the same number or do I just multiply them?

Homework Statement Greetings everyone! I am having problems getting started with this question, which asks: Find the inverse of y = \frac{3-4e^x}{6-10e^x} Homework Equations The Attempt at a Solution I'm usually pretty good with these kinds of problems, but for some reason I seem to be...

Homework Statement Use logarithmic differentiation to find dy/dx for y=(1+x)^(1/x). Homework Equations dy/dx The Attempt at a Solution ln y = ln (1+x)^(1/x) = (1/x) ln (1+x) (dy/dx) /y = (-1/x^2)(ln(1+x) + (1/x)(1/(1+x) dy/dx = y [(-1/x^2) ( ln(1+x) + x/(1+x) ] or (-1/x^2)(...

Homework Statement I'm attempting to prove the rules for the logarithmic function using the Integral definition: Log(x)=[1,x]∫1/t dt. I think I am alright with the product rule but I'm struggling with the quotient rule: i.e. Log(a/b)=Log(a)-Log(b). I believe that I'm having trouble breaking up...

I'm attempting to prove the rules for the logarithmic function using the Integral definition: Log(x)=[1,x]∫1/t dt. I think I am alright with the product rule but I'm struggling with the quotient rule: i.e. Log(a/b)=Log(a)-Log(b). I believe that I'm having trouble breaking up the Integral...

In my complex analysis textbook, there is a definition about log function, which is: log z := Log |z| + i arg z = Log |z| + i Arg z + 2kπ where k = 0,±1,±2... my question is , is there any different between log and Log, and arg and Arg? If yes, what's the different between them

Hi all, I have functions \eta(\mu),Z(\mu) related by \eta(\mu)=-\frac{d \ln{Z}}{d \ln{\mu}} I'm told that if we specify \eta then we have Z^{-1}(\mu)=Z^{-1}(\mu_0)\exp(\int^{\mu}_{\mu_0} dk \ \eta(k)) but upon inverting this equation, taking the log and differentiating wrt \ln(\mu) I get...

Homework Statement [PLAIN]http://img225.imageshack.us/img225/6162/unledsxy.png Homework Equations logb(x)-logb(y) = logb(x/y) logb(x^n) = nlogb(x) The Attempt at a Solution i am stuck on what to do because of the 4-2-2 portion. I've attempted it multiple times to get the...

1. Hello there, I have a few questions on the derivative homework that I did but not sure if it's right or not. These are difficult and my teacher doesn't go over all of them so I don't know if it is right or not. Please help me so I can understand the concepts before the upcoming test. 1...

In most of exercises of textbooks when ask me to differentiate f using logarithmic differentiation some time f(x) = 0 for some values of x , so I I used logarithmic Differentiation for all x in domain of f , such that f(x) not equal zero. then prove using the definition directly that for...

Homework Statement 1. f(n) = log(n) ^ (log(n)). Simplify for Big-O notation. The Attempt at a Solution 1. I'm just trying to prove a big-O notation for one of my courses, and this was simplified to f(n) = n^log(log(n)) And I'm having a hard time seeing why. Any guidance would be...

Homework Statement I have to evaluate the following integral: \frac{\partial \log\rho (r)}{\partial \log r} for \rho (r) = \rho_0 \Big(1+\big(\frac{r}{\alpha}\big)^2\Big)^\frac{-3 \beta}{2} where \rho_0,\alpha,\beta are constants and r is a random variable. Homework Equations...

I am facing difficulty in graphing this logarithmic function: some constant= y + log x what all steps are required to graph such a function?

This is related to differential equations, but I think my question has more to do with log identities than DE. I keep seeing equations like 1/8 lny = t + c simplified to get the solution y = ce^8t but I am unsure of the identity being used to get 1/8 into the exponent as 8. I...

Homework Statement A question asks me to find the first three non-zero terms of ln(cosx) Homework Equations The Attempt at a Solution I wrote cos x as 1+(1-cos x), used the power series of ln function, expanded cosx and simplified, here is my answer: 1/2x^2 - 1/6x^4 + 1/16x^6...

Homework Statement Find first three non zero terms in series expansion where the argument of funstion is small ln(5+p) Homework Equations The Attempt at a Solution The only way I could think how to do this is by saying ln(5+p) = ln(1+(4+p)) and expanding to (4+p)-...

Hello, It has been said if a photon crosses the event horizon of a black hole it will have a spiral orbit; The spiral is Archimedes r = r_{i}+r_{0}\theta^2 There is one such example in "Introduction to tensor calculus, relativity and cosmology" by D F Lawden on page 165 Is it possible...

Hello! I was wondering if they're any identities between exponential and logarithmic functions? Maybe identities isn't the right word, but what I'm talking about is something like euler's formula. Other than than {e^x} and {ln(x)} are inverses, if that counts. Any help is very much appreciative!

Solve for b, f(x)=b^x Here is where I am so far lny=lnb^x lny=xlnb^x y'/y= lnb e^y'/y= e^lnb b= e^y'/y My question is, can I simplify the exponent y'/y any further, or is my answer good here? Thank you

Homework Statement The logarithmic decrement δ of a lightly damped oscillator is defined to be the natural logarithm of the ratio of successive maximum displacements (in the same direction) of a free damped oscillator. That is, δ = ln(An/An+1) where An is the maximum displacement of the n-th...

The problem I am having with these is that I'm sometimes not sure whether to begin differentiating first, or to start taking logarithms - and whether the order changes the outcome For example: Find the equation of the tangent line to the curve at the given point. y= \frac{(e^x)}{x}...

Homework Statement i got stuck at the question below:- Homework Equations The Attempt at a Solution I tried to solve it by simplifying it but i got stuck at:- Please help.

Got a load of Logarithmic Inequalities questions. Solved almost all of them but got stuck in a question. here's the question:- log3 |3-4x| > 2 Please help.

Modeling with exponential and logarithmic functions help? Homework Statement Use Newton's Lay of Cooling, T = C + (T0 - C)e-kt, to solve this exercise. At 9:00 A.M., a coroner arrived at the home of a person who had died during the night. The temperature of the room was 70 degrees F, and at...

Homework Statement S = integral symbol S (e^(2x))/((2+(e^x))^2) dx Homework Equations u = 2+(e^x) (e^x) = u-2 du = (e^x) dx The Attempt at a Solution S [(e^x)(e^x)]/((2+(e^x))^2) dx S [du(u-2)]/(u^2) For the first (e^x) dx I substituted du. And since there was only (e^x)...

I'm stuck on these three maths questions. 1) In a geometric progression, the sum to infinity is four times the first term. (i) Show that the common ratio is 3 (ii) Given that the third term is 9, find the first term. (iii) Find the sum of the first twenty terms. 2) Solve the...

So many of us know that our eyes detect brightness on a logarithmic scale. Something that is twice as bright to us is in fact 2.51x as bright. So I was curious as to other senses for humans are logarithmic? The reason I was wondering is because I was wondering about how accurate you really...

"mixed" logarithmic equation Homework Statement I'm trying to solve for x in the following equation: e^(-66/x)/x^2 = c, where c is a constant Homework Equations The Attempt at a Solution By taking ln of both sides and then dividing by 2, I get to: -33/x -ln(x) = c/2 Then, in order to get an...

I have a very small set of data. Usually 3 points, sometimes 4. Best fit is a logarithmic equation y=m*Ln(x)+b How can I obtain m and b?

Homework Statement Find y' using logarithmic differentiation if y=x^{sin(x)} Homework Equations The Attempt at a Solution lny=sin(x)ln(x) \frac{1}{y}(y')=sin(x)(\frac{1}{x})+ln(x)\cdot cos(x) (y')=[sin(x)(\frac{1}{x})+ln(x)\cdot cos(x)]y Did I do this one properly? Thanks in advance.

Homework Statement Combine into one log log√x + 1 + ( 9log x ) Homework Equations - The Attempt at a Solution I tried converting log√x + 1 to log(x+1)^(1/2)

Homework Statement Simplify log21/8 Homework Equations - The Attempt at a Solution the answer i got was -3 but it is not right.

Homework Statement In a certain experiment, the power (P) radiated by a light bulb filament was measured as a function of the filament's absolute temperature (T). Data: P(W) 0.45 0.95 1.8 3.5 5.6 T(K) 1000 1200 1500 1800 2000 (a) Plot the data (Done) (b) Assume a power...

Homework Statement Determine the equation of the line that is tangent to y=8^x at the point on the curve x=1/2. Homework Equations Differentiation Rules m=y2-y1/x2-x1 The Attempt at a Solution y=8^x dy/dx=8^x(ln8) =8^0.5(ln8) =5.9 y=8^x =8^0.5 =2.8 5.9=y-2.8/x-0.5...

The equation is the following: Log81x + logx3 = 2 I've been bashing my head with change of base but i can't seem to get anywhere with it. 81 is rewritable as 34 which seems like it has something to do with the solution, but i just can't seem to get the hang of it. I always get stuck with...