Log Definition and 618 Threads

Homework Statement Given a^2+b^2=47ab provehat log((a+b)/7)=1/2(loga+logb) The Attempt at a Solution I am assuming it is using multiple log properties... idk how though :|

[SOLVED] log a 3.5= ? given log a 2= 1.8301 and log a 7= 5.0999 what is log a 3.5=? Thanks!

double log scale - please help I am trying to find/create the equation for a straight line on a double logarithmic scale graph - what is the format of the equation or how do I do this using data points from the graph.

1. Convert to logarithmic function: e^3=0.0498 3. ln(-3)=0.0166 is my guess

Homework Statement Find y' y=ln(x^2 + y^2) Homework Equations d/dx ln(u)= 1/u du/dx The Attempt at a Solution y' = [1/(x^2 + y^2)] (2x + 2y) y' = (2x+2y)/(x^2 + y^2) But my book says the answer is 2x/(x^2 + y^2 - 2y) How can that be?

It seems to that i went wrong way. Homework Statement \int \frac{arcsin(e^x)dx}{e^x} The Attempt at a Solution =-\frac{arcsin(e^x)}{e^x}+\int \frac{dx}{\sqrt{1-e^{2x}}} \int \frac{dx}{\sqrt{1-e^{2x}}}=\frac{x}{\sqrt{1-e^{2x}}}+\int \frac{xe^{2x}dx}{(1-e^{2x})^{\frac{3}{2}}}

**Im helping a friend go through this problem, so "the answer will be shown eventually" because I am editing as we go through. Homework Statement 2^{x-1}=25Homework Equations All Log/Exponent Formulas, they'll be shown as we go. The Attempt at a Solution There are various ways of approaching...

Homework Statement log_u (5) = a; log_u (27)=b; log_u(32)=c what is the numerical value of u^(2a+(1/3)b-(2/5)c) Homework Equations The Attempt at a Solution Can you do (u^2a * u^(b*1/3) ) / ( u^(c*-2/5))) and then do log_u of the whole thing from here can you make it ((u^a)^2 *...

Homework Statement Prove that f(n) = n * log (n) is O(n(1+sqrt(n))). Homework Equations n/a The Attempt at a Solution I really don't know what to do else I wouldn't be here :? Some hints would be appreciated!

Hello Im studying an ATS equipment known as an ILS. One of the formulas to determine the DDM is : E[SIZE="1"]2 = E[SIZE="1"]1 log-1(db/20) When I try entering log-1, the calculator displays Math Error. What am I doing wrong? Thanks for the help in advance

Homework Statement 2^x=1500. solve for x. I need to know the key strokes on my scientific calculator. If I push log, it assumes log base 10. I need base 2. Homework Equations The Attempt at a Solution

Homework Statement Solve for x: log(x+5)= log x + log 5. Homework Equations log a + log b = log (ab) The Attempt at a Solution log (x+5)= log (5x) x+5= 5x 4x=5 x=5/4 However, my question is: When you make the logs to the power of 10, to eliminate them, do you always...

Hi, I've been trying to work out: loga(2+x) = 2 + logax This is as far as I can get: loga(2+x) - logax =2 so: loga((2+x)/x) =2 loga((2+x)/x) =log100 (I'm not even sure where I could go with this one though). Relevant equations include: log x +log y = log xy log x - log y = log x/y...

Problem: If 2^{x}=3, what does 3^x equal? I solved this by taking the log_{2} of both sides. However, the book's solution involves taking the natural log of both sides. Can someone show me why that would work? I don't get what the x power changes to a x term. The natural log is base 10 right?

Homework Statement I'm supposed to evaluate the following series or show if it diverges: SUM (sigma) log [(x+1)/x] Homework Equations Drawing a blank...:confused: The Attempt at a Solution I'm unsure how to start this. We've gone over all sorts of tests for convergence (ratio, comparison...

I'm having real problems integrating a natural log. The problem I have been set is (where S = integration sign) S (x - 2) Ln(3x) I'm trying to use the integration by parts rule but keep getting the wrong answer and I think it might be to do with the natural log. I have used f(x) =...

If we have a function of the form Ln(ax) Is it the case that the derivative is simply 1/x no matter what the initial value of 'a' might be? Or do we take into account 'a' in some way The thing i need clarifying is this... If we have Ln(3x), the derivative is 1/x, but the integral of...

Hi. Could someone please help me with the following questions? I'm totally stuck so any feedback would be really appreciated. I'll post the questions one at a time. Express as single log. functions: (i) ln (x + 1) - 3 ln (1 - x) + 2 ln x I got up to ln ( (x + 1) / (1 - x)^3 ) / ln...

Homework Statement the indefinite integral of (1+lnx)^(1/2)/(xlnx) dx Homework Equations n/a The Attempt at a Solution There aren't any x^2 in the root sign, so I don't think it can be a trig substitution. The only logical u sub I see is to let u=lnx. In that case, du=dx/x so the...

What is Log e ? (log sub e) Where would i find it on a calculator?

Homework Statement (Idk how to put in the equation to make sense, therefore it is at the link below) Homework Equations The Attempt at a Solution Here is all I have done. Something just isn't right...there should be 3 answers (in the back of the book) because there is a cube...

Basic log question, completely lost! :( Homework Statement Prove that y = a(1+b)^t is equivalent to ln y = a+bt Homework Equations The Attempt at a Solution i'm really confused with how they could possibly be equal. y = a(1+b)^t t = ln y/ln a(1+b) ln y = t x ln (a+b) ln y...

Can you get logarithms of imaginary numbers? The reason I was wondering is because integrating 1/(1+x^2) WRT x. I know the answer is arctan(x), but how about breaking it into partial fractions by doing 1/(1-ix)(1+ix)?

Homework Statement Solve the equation: 2^x multiplied by 4^(x + 5) = 4^(2x - 1) Homework Equations The Attempt at a Solution 2^x multiplied by 2^2(x+5)=2^2(2x-1) x(2x+10)=4x-2 2x^2+10x=4x-2 and that's as far as i could get before I was completely stuck. But this could be...

Homework Statement Solve for Y in terms of X Homework Equations 2log_5X/ log_53 - log_5Y = 2 The Attempt at a Solution I know all the properties of logs, i just don't know how to apply them to this problem. The answers in the book are . y = 1/25x^2/log_53 When i am...

Homework Statement the question asks to graph the equation: (don't know how to use latex sorry) f(x) = log5 (x) + 3 where the 5 is the base Just for my curiosity what would the exponential equation be? I can graph it, just can't get the exponential form Tell me if this should go in the...

I was working on an experiment for the vapor pressure of water and I have the following formula ln (p) = -L/(RT) + ln (p_o) L=heat of vaporization of water R=Molar gas constant T=temperature in Kelvins I have some data points for the pressure p in units of mm Hg, when I take the...

Can someone explain to me when to use natural log or common log? I understand that natural log gives creates a base e and the common base 10 but i don't understand why there are 2 different ones.

Hi, To solve the following d.e.: xdy-ydx = 0 1 you get ln(y)-ln(x)=C 2 no clearly you can simplify to: ln(y/x)=c 3 which after taking exponentials gives: y=Ax where A=e^c 4 however what interests me is if you do not simplify...

Homework Statement log base 5 cube root 25 equals what? Homework Equations I know that the answer is 2/3 because it is in the back of the book The Attempt at a Solution log base 5 = 25 to the 1/3 so 5 to the what = 25 to the 1/3 How do I get 5 to the 2/3 equals 25 to the...

Hi, I come from an engineering background and so have not studied analysis (sadly). I need to figure out the following. How does: 1.) x^y*|ln(1/x)|^m behave for any m given y<0 as x-> infinity 2.) x^y*|ln(1/x)|^m behave for any m given y>0 as x-> 0 The way I see it in the...

Here we go again. Another layer has been added to the Bush administrations unprecedented record of secrecy. http://www.guardian.co.uk/worldlatest/story/0,,-6325579,00.html

How would one go about solving for C in the following equation? log ( A - B - C ) = -C + A + B I have done this... log ( A - B ) / log ( C ) = -C + A + B Then... C + ( log ( A - B ) / log ( C )) = A + B But I am just shooting in the dark really. Where would one go from here...

Homework Statement find dy/dx for y=ln(sec^(2)x) Homework Equations none The Attempt at a Solution 1.)1/(sec(x)^2)*dy/dx sec(x)^2 2.)tan(x)/sec(x)^2 3.)i put it in terms of sin and cos... sin(x)/cos(x)*cos(x)^2/1 4.)i canceled the cos(x) in the denominator and came...

I have the problem 3e^(x+2) = e^(-x) and I need to find X. It's been a while since I've looked at any Calculus 2 stuff so I am not sure on what to do here. I take the natural log of both sides LN(3e^(x+2) =LN(e^(-x))= (x+2)ln3e = -xlne So (x+2)Ln3e= -x Where do I go from here?

Homework Statement When you walk along a floting log in water, why does it move in the opposite direction? Is it because of the friction from you walking pushes the log in the opposite direction, or is there something else?

Homework Statement A round wooden log with a diameter of 83 cm floats with 72% of its radius out of the water. What is the log's density? answer unit is kg/m3 Homework Equations density of water= 1000 kg/m^3 The Attempt at a Solution I've tried to find the area that is exposed, but...

Having some trouble understanding derivatives including numbers to the "X" power. For example, f(x)= 7^8^x, f'(x)=? help please!

Natural Numbers - Pi, Log, ... Greetings, I'm far from an expert on math and I wanted to appeal to smarter minds to help compile a list of numbers with non-repeating chaotic decimals: Here's the first 2 (the only 2 I can think of) Pi e I'd also include the order of prime numbers...

Hello everyone. I'm stuck on this problem and not sure how to apply the Unique factorization therem also called (Fundamental Theorem of Arithmetic). Heres the problem: http://suprfile.com/src/1/45ym0fx/lastscan.jpg The back of the book gives a pretty big hint which is the following...

Hi, In his notes, our teacher makes this approximation: \log(1 + 3e^{-2\frac{E_o}{\tau}}) \approx \log(3e^{-2\frac{E_o}{\tau}}) For \tau << E_o Also, and I don't think this matters, the logs are assumed to be natural logs. I was wondering what the justification for this was...

find the solution(s) to 2e^2x = e^x its on a practise exam I am doing. i did with my calculator, but how could this be done without a calculator?

Here are some log questions that I don't really have any idea how to do. I'd appreciate any hints/help... (solve for x in all questions) 1. 2^x + 4^x = 8^x All I could think of doing was converting them to the same base. I don't see how to simplify the left side of the equation so I can...

A boat floats across this river, and back, It takes 5 hours for it to reach point B, from point A, and then 7 hours to return to point to point A from point B. Naturally it's because not because the crew got tired on the way back, but because the flow of the river, or it's angle which is...

A log weighs 800N and has its center of gravity at the midpoint. Find the lowest coefficient of static friction necessary to keep the log from slipping. Answer (1.01) http://img115.imageshack.us/img115/8407/physicsproblem3ox.th.png Ok, so, i started out by finding my torque and force...

Find the first derivitive. Simplify if possible (factor). \begin{array}{l} y = x^{e^x } \\ \\ \ln y = \ln x^{e^x } \\ \\ \ln y = e^x \ln x \\ \end{array} There's a similar problem in my class notes where it was solved by taking the natural log of both sides. Is this...

Hey Integral, Did I log off my PF account on your computer?

I graphed y=logx+log2x and y=log2x^2 and the graphs came out a lot different. However when you simplify y=logx+log2x you actually get y=log2x^2! Any ideas about why the graphs are so different yet the equations are pretty much the same? thanx

Here is a problem that I was presented in my math class using logs and my entire group is stumped: Peter deposits $800 into an investment fund that earns 8% per year, compounded annually. Mary Jane deposits $1000 into an investment fund that earns 6% per year, compounded annually? When will...

this problem is an excerpt from an explanation of a time wieghted performance method. I feel that if I can follow this part the rest of it will make sense. now i know the answer is .1259 but I'm a little fuzzy on how exactly they got that, and their 'step by step' seems to miss some steps. it...