What is Log: Definition and 632 Discussions

In science and engineering, a log–log graph or log–log plot is a two-dimensional graph of numerical data that uses logarithmic scales on both the horizontal and vertical axes. Monomials – relationships of the form



y
=
a

x

k




{\displaystyle y=ax^{k}}
– appear as straight lines in a log–log graph, with the power term corresponding to the slope, and the constant term corresponding to the intercept of the line. Thus these graphs are very useful for recognizing these relationships and estimating parameters. Any base can be used for the logarithm, though most commonly base 10 (common logs) are used.

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  1. R

    Derivative of metric and log identity

    Has anyone seen this identity: g^{ab}\nabla g_{ab}=\nabla ln|g| I've seen it used, but want to figure out where it comes from. Does anyone know a name or have any ideas??
  2. D

    Frictional forces acting on log Application of Newtons Laws

    A rope is tied to a 97.8 kg log. When you pull on the rope with a horizontal force of magnitude 706 N, the log moves at constant speed. a) Find the magnitude of the resistive (frictional) force acting on the log. You may assume the frictional forces acting on the log is constant. N b)...
  3. D

    Average of Log of a Function: Bounded by 1 and Convex

    Hello, I am interested in the average behaviour of the log of a function. I know the average of the function over the range of interest: F = \frac{1}{(b-a)} \int_a^b f(x) dx. I also know that f(x) is convex and bounded from below by 1. I want to know the average \frac{1}{(b-a)}...
  4. S

    Finding Units of k in t = k√(h)/d² Equation | Log-Log Graphing Question

    Question asked to find the units of k after you find the porpotionality statement i ended up getting t\propto\frac{\sqrt{h}}{d^2} so i turned that into an equation and end up with t=k\frac{\sqrt{h}}{d^2} solved for and found it on average to be 30 now the question is asking what the...
  5. F

    Limit involving natural log

    Homework Statement Find the limit of (tanx)^cosx as x-->infinity Rearrange the equation so that you can use L'Hopital's rule for the form of (infinity/infinity) The Attempt at a Solution I did ln(tanx)^cosx = cosxlntanx I know the limit of tanx as x-->infinity is pi/2 the limit of cosx as...
  6. B

    Natural Log of negative number

    I've got a simple question that's been bugging me for a while. I think I know where the problem is, I'd just like a formal mathematical reason why I can't say this: \ln{(-1)}^2 = \ln(1) = 0 That part is fine...but then: \ln{(-1)}^2 = 2 \ln(-1) = 2 (i \pi) when they should...
  7. D

    Newbie Seeks Math Assistance: Log Questions & Calculus Textbooks

    [SOLVED] Help a newbie! Hey everyone. This will be my first post. A little background info: I have a bit of math anxiety due to doing very poorly with it in school despite a bit of effort. I had finished college in May with a degree that required only Statistics. My last year, I had...
  8. M

    Logarithmic Scale Calculation | Ritcher Scale Homework Example

    Homework Statement See image Homework Equations M = log(I_i / I_o) The Attempt at a Solution See image
  9. Andre

    Log, Rock & Scissors: Nature's RPS

    Roshambo is the name for a popular two-person hand game. It may also be referred to as Paper, Rock, Scissors. Rock blunts scissors, scissors cut paper, paper folds around rock. Nature plays it too. But instead of paper it uses logs: Log folds around rock...
  10. C

    Natural Log and Inverse derivatives

    Homework Statement Let f be the function given by f(x) = ln [ x/ (x-1)] (a) What is the domain of f? (b) What is the value of the derivative of f at x = -1. (c) Write an expression for f^(-1) of x, where f^(-1) denotes the inverse function of f. The Attempt at a Solution a. x / x-1...
  11. C

    Intensity Increase for 30dB & 22dB: Log Homework Solved

    Homework Statement A hearing aid increases the sound intensity level, thereby allowing a person to hear better. For the following decibel increases, by how much does the intensity of sound increase? a)30dB b) 22dB Homework Equations \beta=10log (I/Io)The Attempt at a Solution I substitute...
  12. Z

    How Is the Integral of Natural Log of x Calculated?

    can someone please explain this to me?
  13. K

    Solving Log Equations: How to Use Logarithmic Properties | Homework Help

    Homework Statement Solve the equation log base 7 (7x+8) = log base 7 (7x+3) Homework Equations I don't think you use equations for this, just the properties of logarithms The Attempt at a Solution I thought since they have the same base you could set the parts in parenthesis equal to each...
  14. S

    Logarithmic Properties in Proving Equations

    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 :|
  15. J

    Log a 3.5: Finding the Solution using Logarithmic Rules

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

    Double Logarithmic Scale: Find/Create Equation

    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.
  17. S

    Can e^3 be converted to a logarithmic function with a value of 0.0498?

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

    What is the derivative of ln(x^2 + y^2)?

    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?
  19. A

    How to Write arcsin in Log Form for Integration

    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}}}
  20. M

    How Do You Solve for X in the Equation 2^(x-1) = 25 Using Logarithms?

    **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...
  21. P

    Numerical value and log problem

    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 *...
  22. L

    Prove that f(n) = n * log (n) is O(n(1+sqrt(n))).

    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!
  23. M

    Troubleshooting Log Formula for ILS DDM Calculation | Expert ATS Assistance

    Hello Im studying an ATS equipment known as an ILS. One of the formulas to determine the DDM is : E2 = E1 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
  24. S

    How Do You Calculate Log Base 2 on a Scientific Calculator?

    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
  25. L

    Solve for x: Log (x+5)= Log x + Log 5

    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...
  26. C

    Can you help me solve this logarithmic equation: loga(2+x) = 2 + logax?

    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...
  27. L

    Solve Natural Log Problem: 3^x when 2^x=3

    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?
  28. R

    Convergence or divergence of log series

    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...
  29. B

    How can I integrate (x-2)ln(3x) using the integration by parts formula?

    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) =...
  30. G

    Derivative of Natural Log - How Does 'a' Affect the Derivative of Ln(ax)?

    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...
  31. C

    How Do You Simplify Complex Logarithmic Expressions?

    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...
  32. M

    Irrational natural log integral

    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...
  33. G

    Exploring the Natural Logarithm: Understanding Log e on Calculators

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

    Why Am I Getting Incorrect Solutions to This Logarithmic Substitution Problem?

    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...
  35. C

    Basic log question, completely lost

    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...
  36. T

    Log of i: Can you get logarithms of imaginary numbers?

    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)?
  37. C

    Solving Log Equations: 2^x * 4^(x+5) = 4^(2x-1)

    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...
  38. I

    Can someone give me a hint please for a log question

    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...
  39. W

    Converting a log equation to exponential equation

    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...
  40. mattmns

    Number Theory - Discrete Log (Index) - Equation

    Here is a silly question from our book, that seems to be a pain to solve: ------------ Solve the following equation: 59^x \equiv 63 \ \text{mod 71} ------------ The idea is to use the discrete log (or index). Note that 7 is a primitive root mod 71. The two books I have looked at...
  41. K

    What's the UNIT after you take the natural log?

    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...
  42. D

    When should I use natural log vs common log in scientific calculations?

    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.
  43. B

    Solving Log Equations: No Simplification Needed

    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...
  44. G

    Solve Log Question: Find Cube Root of 25 in Base 5

    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...
  45. B

    Solving Basic Log Question: x^y*|ln(1/x)|^m

    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...
  46. edward

    News Whitehouse visitor log now unavailable to public

    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
  47. J

    Having trouble with this log equation `

    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...
  48. T

    Why Does Differentiating ln(sec^2(x)) Yield an Unexpected Result?

    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...
  49. C

    How to Solve a Natural Log Question for X: Step-by-Step Guide

    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?
  50. F

    Discover the Science Behind Floating Logs: Exploring Opposite Direction Movement

    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?
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