Logarithmic Definition and 355 Threads

Hi :) This is my first time using this forum, so thanks for your help in advance. Homework Statement Use the laws of logs to write y as a function of x for each. Then state domain. a) log(xy) = 2 log(x-3) b) log(y) + 3 = log(y + 1) + log(x) c) log (x2/y) = 2 log(x + 5) Answers: a)...

Hi all! From time to time, I work as a math tutor. Normally this doesn't cause me any trouble, but a couple of days ago a student from an IB school came to me with this problem: 2*5(x+1) = 1 + 3/(5x). Solve for x and write the solution on the form a + log5b. I've been trying to solve...

Hi everyone - I'm in my first year at uni, and I was given a derivative that i don't quite get: y(x) is a function of x then y` = (dy/dx) d/dx (ln y(x))=1/y(x)*(dy/dx) =(y`/y) This is given by the chain rule. I don't understand this step... Any help? Thanks in advance, Owen.

Homework Statement y = 5ln(7lnx) Homework Equations y' = 5 x 1/7lnx +97lnx0 x 1/x = 5(7lnx)/7lnx + 5ln x 7/x The Attempt at a Solution y' = 5 + 35ln/x is this right?

Homework Statement Using logarithmic differentiation calculate the derivative of y=e^(x^x) The Attempt at a Solution y=e^x^x LNy=LNe^x^x LNy=x^xLNe ... Stuck! This seems to be the only way you can do it, but once I get to that part I'm not sure what else there is to do. I...

Hi all, Does anyone know how to get Mathematica make a 3D plot with logarithmic axes? I need a, say, 3D version of LogLogPlot. I have a 3D function Rdb[nf, pf] which I want to plot for {nf, 10^10,10^18} and {pf, 10^10,10^18}. I can get cross sections of what I need when I do...

Homework Statement (1.024)^2 = (1 + m)^12 Homework Equations The Attempt at a Solution 1.048576 = (1+m)^12 I tried to do a square root of 12 for both sides but does not appear to be correct. I've also tried doing log to bring the exponents to the front for both sides, but...

Homework Statement Solve the inequality: e^(2-3x)>4 Homework Equations none The Attempt at a Solution would i start of like this? e^(2-3x)>4 ln(2-3x)>ln4 if so how do i continue?

Homework Statement There are two log properties that I have to prove: 1) Explain why ln(b1/n)=(1/n)ln(b) for b>0, set b=an 2) Explain why ln(ar)=rln(a) for any r in Q and a>0, ie r is rational. Homework Equations ln(an)=nln(a) The Attempt at a Solution In a previous question...

I am unsure of how they were able to change 8.7 to 8 and make -2.3 to 2. Whats the explanation behind this?

Homework Statement 4 1/(x+1) · 8 1/(x+2) = 9log3 2 Homework Equations n/a - same as 1 The Attempt at a Solution To get rid of the exponents and be able to solve for x, I first took the logarithm with base 4 of all terms: log44 1/(x+1) · log48 1/(x+2) = log49 log3 2 This equals: 1/(x+1)...

Calculus Logarithmic Functions help please! The question is: A particle moves alonge the x-axis with position at time t given by x(t) = e^(-t) sin t for 0 ≤ t ≤ 2π. 1. Find the time t at which the particle is farthest to the left. Justify your answer. 2. Find the value of the constant A...

Homework Statement I have 2 problems ,which are: 1) Solve :log 7 (x 3+27) + log 7 (x+3) 2) Solve for x:log5 ( 5 1/x+ 125) log 5 6+1+1/2x Homework Equations The Attempt at a Solution The first one tried like this : log 7 { (x 3+27)/(x+3) }= 2 or 7 2 = (x 3+27)/(x+3) But...

Does anyone know how to solve this integral? int. (ln(ax+b))^2 Struggling! Thanks :D

I'm discussing decompression in shallow water. I never studied logarithms. At sea level, a diver is at 1 atm, at 33ft: 2atm, at 66ft: 3atm. How does it work between 33 and 0? Specifically, at what depth is 1.25atm? Is it less than 8.25ft or more than 8.25ft?

Homework Statement Evaluate the expression "log base 8 of 16" Homework Equations Don't know of any The Attempt at a Solution I don't know where to begin. I have read the textbook chapter on logarithms three times over, and I am now more thoroughly confused than ever. My textbooks...

Homework Statement Note this is exam revision rather than actual course work worth marks, so there is no need to be deliberately vague :) The question comes in two parts, regarding a lightly damped harmonic oscillator with frequency 10 kHz and an amplitude that decays by 25% over 300...

Homework Statement My book has these steps for evaluating a logarithmic equation and I don't quite understand what is going on. It says... log (2) x(x-4)=5 x(x-4)=2^5 <---------> this is the level I am getting problems... how does log(2) divide the 5 on the other side and end up getting...

Homework Statement Calcualte the value of \int\limits_L \sqrt{x^2+y^2}dl, where L is an arc of a logarithmic spiral r=ae^{m\phi} between points A(0,a) and B(-\infty,0). Problem: I can't find a value of \phi where x=-\infty or y=a. Homework Equations We parametrise and get...

Homework Statement 1. Use the fact that loga(10)= 2.4197 and loga(13)=2.6955 to solve the following a. loga(130) b. loga(1.3) c. loga(1000) Homework Equations The Attempt at a Solution I'm not really sure how to do this i missed yesterdays class i don't really want...

Homework Statement Basically, I have LQ''(t) + RQ'(t) + (1/C)Q(t)=0, and I'm supposed to "Show that the ration of the charge Q between two successive maxima is given by exp(RTd/2L), where Td is the time between two successive maxima. The natural logarithm of this ration is called the...

Homework Statement Differentiate the following: y = e4x/x2+1 2. The attempt at a solution I know you have to use quotient rule here. so I wrote out (x2+1)* d/dx e4x) - d/dx (x2+1)* e4x all over (x2 + 1) 2 I have no idea how to continue on from here...how would you...

Homework Statement Simplify (\log_a{b})(\log_b{c})(\log_c{d}) in terms of \log_x{y} Homework Equations The Attempt at a Solution well , the furthest i can reach is \frac{\log_xd}{\log_xa} , how do i express in terms of \log_x{y}

I was trying to evaluate this integral, \int\frac{dx}{\ln x} I substituted x=e^{i\theta} and I get, \int\frac{e^{i\theta}}{\theta}d\theta which is, \int\frac{\cos \theta}{\theta}+i\frac{\sin \theta}{\theta} \ d\theta \int\frac{\cos \theta}{\theta} \ d\theta+i\int\frac{\sin...

how can logarithmic divergences be renormalized ? for example if i have \int_{0}^{\infty} \frac{log^{n}(x)dx}{x+a} differentiation with respect to 'a' and integration over 'x' gives finite result for example \int_{0}^{\infty} \frac{dx}{x+a}=-log(a)+C here 'C' would be an extra...

The logarithmic integral function, which is what you get by integrating 1/ln(x), is closely linked to prime numbers. It approximates the number of primes smaller than x. Heres an infinite series which describes the function: li(x)=\gamma+ln(ln(x))+\sum^{\infty}_{n=1}\frac{ln(x)^n}{n*n!}...

Homework Statement see attachment Homework Equations log10x=y 10y=x The Attempt at a Solution Since I'm rather confused on reading a logarithmic scale, I thought I'd post this to see if I'm doing this right and/or if there's a better way to do the problem. a) T=500 C using the...

So I was playing around with logarithmic & exponential amplifiers in my lab class. I was looking at the following equations: http://upload.wikimedia.org/math/7/7/6/77663157d5b97ceb2e3edac5f587a620.png and http://upload.wikimedia.org/math/b/3/c/b3c569c85552561e41dec916f6e8ebe8.png...

Hi! I'm making a computer program that represents some quantities in a graph in this way: x'i=(xi-xmin)/(xmax-xmin) so that the possible values of x range from 0 to 1. This is a linear scale. I want to do the same with the logarithmic values of xi. That is, I want to implement a log...

Can anyone please tell me what is wrong with this solution log(5x-17) = log(4x-14) As logarithmic functions are one-one so, 5x-17 = 4x-14 => x =3

can someone please explain the difference. Graphically and mathematically it is easy to see they are inverses. But I see certain scales like the Richter scale that seem to increase exponentially, but are labeled as logarithmic scales. for example, on the richter scale with each increase in...

Homework Statement Compute the derivative: d/dx log base 10 (x^3 + x^2) Homework Equations The Attempt at a Solution (3x^2 + 2x)/(ln 10)(x^3 + x^2) seems a little off.. not sure though thanks for the help in advance! (:

Homework Statement logx13-3log13x=-2Homework Equations n/a The Attempt at a Solution (log13/logx)-(3logx/log13)=-2 What do I do next?

Homework Statement 4x + 2(x+1) = 60 Homework Equations N/A The Attempt at a Solution 4x + 2(x+1) = 60 22x + 2(x+1) = 60 I don't know where to go from there.

lim_{i\rightharpoonup\infty} \frac{ln(4^{i}-1)}{ln(2^{i})} If I set this up right it should go to 2, but I'm pretty rusty and every time I try to work this out I end up getting garbage or repeating behaviors that I can't do anything with... Anyone know what exactly to do with it? edit: Ack...

6throute (x-7) -------------- log11(13-x) What is the domain of the function in interval notation. I know to set x-7 > 0, so that gets me x>7 , and I know I have to set 13-x > 0, which gets me x < 13. But the notation that is correct is [7,12)U(12,13). Where do you...

find derivative of y=(sqrt(8x^4-5))/ (x-1) ok...after working out the tricky calculations i get for my final answer: (32x^4sqrt(8x^4-5)-64x^3sqrt(8x^4-5)) / (16x^6-32x^5+ 16x^4-10x^2+20x-10) I don't know if you want to do the math...im just wondering if i can simplify it anymore. thanks

Homework Statement Use the properties of logarithma to xpand the logarithmic function ln[(x2+1)(x-1)] Homework Equations The Attempt at a Solution [ln x2+ln 1]+[ln x-ln 1] 2 ln x+ln x

Homework Statement http://img20.imageshack.us/img20/1476/mathproblemi.jpg Homework Equations Properties of logs. The Attempt at a Solution For the first two I did: Int( \frac{Log(2)}{Log(1.1)} ) Doing this resulted in the correct answers for the first two boxes. When I...

Homework Statement y=9-x Homework Equations The Attempt at a Solution dy/dx=-9-xln9 We are provided with the answers. I do not understand the concept behind how to get from the question to the solution. What rule(s) are applied? If somebody could solve this single question...

Homework Statement Show that the function Log(-z) + i(pi) is a branch of logz analytic in the domain D* consisting of all points in the plane except those on the nonnegative real axis. Homework Equations The Attempt at a Solution I know that log z: = Log |z| + iArgz + i2k(pi)...

simplify the following expression log2 4^3x-1 (2 is a subscript of log and 3x - 1 is a superscript of 4) i can rearrange this to 4log2 3x - 1, i am thinking after this it becomes 4 log3 + 4 logx, but i don't know what to do with the -1 please show all the steps and explain.

Homework Statement Find an equation of the tangent line to the curve $\displaystyle \Large y = (2 x^2+5 )\ln (4 x^2-3 )+7$ when x = 1. Homework Equations $\displaystyle \Large y = f'(x_0)(x-x_0)+f(x_0).$ The Attempt at a Solution the fact that the tangent line to the curve y =...

Homework Statement Hi, Our professor has only taught us these methods for Integration...thus far: Direct Integration Substituion Method So theoretically we should be able to solve this problem without using Integration by parts or partial fractions...: Integrate...

Homework Statement \int^{e^2}_{e} \frac{1}{xlnx} dx Homework Equations The Attempt at a Solution I substituted U= xlnx So DU= (\frac{1}{x}dx...so Du * X = 1dx From there I am stuck!

what is the integral of the function 1/lnx?

the idea is let us supppose we have a well behaved theory where only logarithmic divergences of the form \int_{0}^{\infty} \frac{dx}{x+a}=I(a) for several values of 'a' occur , then would this theory be renormalizable ?? , i think QED works because only logarithmic divergencies appear ...

Homework Statement The amplitude of a torsional vibration decreases so that the amplitude on the 100th cycle is 13% of the the amplitude of the first cycle. Determine the level of damping in terms of the logarithmic decrement. Homework Equations The Attempt at a Solution Is this...

The amplitude of a torsional vibration decreases so that the amplitude on the 100th cycle is 13% of the the amplitude of the first cycle. Determine the level of damping in terms of the logarithmic decrement. Is this simply ln(100/13)= 2.04 or ln(13/100)= -2.04?

log9 (p) = log12 (q) = log16 (p+q) What is q/p? 9^x + 12^x = 16^x calculate x (4/3)^x = q/p I guess that would work if I'd know how to solve that equation (without using a calculator), unfortunately I don't... 3^(2x)+4^x*3^x = 4^2x