Log Definition and 632 Threads

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. W

    Integration of a natural log and polynomial

    Homework Statement Evaluate the integral when x > 0: indefinite integral of ln(x2+19x+84)dxHomework Equations I know I need to use some form of integration by parts: integral of u*dv=uv-(integral of(du*v)) The Attempt at a Solution I began by making u=ln(x2+19x+84) and dv=dx. Thus, (after...
  2. E

    How Do You Solve Complex Logarithmic Equations?

    Homework Statement Problem 1: Solve log(x^3) = (log(x))^2 for x. Note, there are two solutions, A and B, where A < B. A = ? B = ? Problem 2: Rewrite the expression 2log(x)-2log(x^2+1)+4log(x-1) as a single logarithm log A. A = ? 2. The attempt at a solution Problem 1 Attempt: I...
  3. E

    Solve x: Calculus Natural Log Homework Statement

    Homework Statement ln(3x+1) = 3-lnx Homework Equations Solve for xThe Attempt at a Solution Well I put the ln on the left side ln(3x+1)+ln(x) = 3 Then I combine them ln ((3x+1)(x)) = 3 So I take e e^ln(x(3x+1)) = e^3 I get x(3x+1) = e^3 So I divide the x (3x+1)/(x) = (e^3)/(x)...
  4. H

    Can Excel be Used to Solve Logarithmic Equations with Different Bases?

    Homework Statement 9 log3(2x+1) + 4 log2(x+3) = 85. Find x! Homework Equations logarithm The Attempt at a Solution I have tried few things but useless. Do not know what to do with different bases. I also tried to change the RHS: 85 = 5 x 17 but nothing worked. Thank you very much
  5. G

    Expected value of the log of a uniform distribution

    Homework Statement How to calculate the expected value of the log of a uniform distribution? Homework Equations E[X] where X=ln(U(0,1)) The Attempt at a Solution integral from 0 to 1 of a.ln(a) da where a = U(0,1) = -1/4 However I know the answer is -1
  6. K

    Unveiling the Mystery of O in F = F0 + kBT log c + ½ cb1 + O (c2)

    Please, This equation is based on the free energy of perfect gaz : F = F0 + kBT log c + ½ cb1 + O (c2) ½ cb1 is the excluded volume term (c is the concentration) but what is O ?
  7. F

    Solving ln(x)=b x^2 for Exactly One Solution

    the question is simple but i can't seem to think of a solution. for what b>0 does ln(x)=b x^{2} have exactly one solution, and not 0. I've tried playing with ln rules but can't seem to think of a solution
  8. C

    Nonhomogeneous Second Order ODE containing log

    Hi guy, I have this ODE that I'm having problems with y"+4y'+4y= e^(-2x)logx Now, Using method of UC to get rid of the RHS I've tried using Ae^(-2x) x^2 logx However, I'm not quite sure whether that is correct or not as I have never had a question containing logs before
  9. Z

    Accelerometer Data Log: Record 8 Variable Voltages

    Hello. I am quite new here and need a little bit of help with an invention I am working on. I'll try to just ask for help on different parts as to not have you guys actually invent it, unless someone is interested in an investment relationship. anywhoo... First off, I have 8 variable voltages...
  10. J

    How do I do log to the base 2?

    On my calculator I have a log button which is log to the base 10 and I also have a natural log button. How do I input log to the base 2 on a calculator? So far the only way I know is to go log(x)/log2 = y for instance if I'm trying to find log to the base 2 of the number 24 I go...
  11. B

    Differentiation of log function

    Homework Statement Find an equation of the tangent line to the curve at the given point. y = ln(xe^(x²)) P=(1, 1) The Attempt at a Solution I know how to plug in the numbers into the Point-Slope formula once I find the derivative of the function, or slope, I'm just not sure...
  12. A

    Natural Log Composed with Hyperbolic Tangent & this Ratio

    Hello, Consider x \in (0,1) , that is x between 0 and 1. Can someone explain why the following is true: \frac{x-1}{x+1} = \tanh \left( \ln \left( \frac{x}{2} \right) \right)
  13. L

    What is the Product Log and how can it be expressed as a closed-form expression?

    What Product Log Means?? Hi, I have the following equation: B = (k*a*Exp[-t*(B/N)*T/beta] - N)/(a*Exp[-t*(B/N)*T/beta]) Using Mathematica, I tried to solve it for B. Mathematica returned the following solution: B = k-(N*beta*ProductLog[(E^((k*t*T)/(N*beta))*t*T)/(a*beta)])/(t*T)...
  14. M

    Estimating area under a curve in log scale

    Homework Statement Hi guys, I'm stuck on this question in exam revision: I need to estimate the area under the following curves (I don't have the equations of the curves) http://img819.imageshack.us/img819/3249/question.jpg The curves are magnitude diagrams in the log-log scale...
  15. mnb96

    When does derivative of complex Log exist?

    Hello, if I have a function f:\mathbb{R}\rightarrow \mathbb{C}, what are the conditions on f for which the derivative of the Logarithm exist? \frac{d}{dx}\mathrm{Log} (f(x)) exists? Note that here I defined: Log(z)=\log |z| + Arg(z), where -\pi< Arg(z) \leq \pi
  16. F

    Trigonometric integration with natural log

    Homework Statement integral of secxtanx/secx -1 Homework Equations sec u du = ln |sec u +t an u | + c The Attempt at a Solution sec u +tan u | + c
  17. F

    How to Use Log Rule for Integrals with Radical Expressions?

    Homework Statement integral of x/square root of 9- x^2 Homework Equations 1/x dx= ln |x| + c The Attempt at a Solution 3 ln|x| + c
  18. B

    Complex log and Winding Number in Pi_1(S^1)

    Hi, everyone: I am confused about the def. of winding number of a loop on S^1 ( on elements of Pi_1(S^1,1) ). The winding number is defined by w(f):= [log(f)1)-log(f)0)]/i2Pi One of the problems is that log cannot be defined continuously on S^1, since complex logs can only be...
  19. K

    Estimating ln n and Proving its Limit as n Approaches Infinity

    Homework Statement using the following definition: ln x = \int dx/x, give best possible upper and lower estimates of ln n, n a positive integer. then, use this result to show that the limit of the function as n approaches infinity is infinity. Homework Equations -- The Attempt...
  20. L

    What does the log likelihood say?

    Hi, here's some information after fitting measurements to a lognormal distribution. What exactely does it mean that the log likelyhood is -67.175?? As of my understanding the log likelihood, is the natural logaritm of the likelihood function, which is the probability that these measurements...
  21. F

    Ln vs. log in Short Calculus book by Serge Lang

    Homework Statement I've been going through a book called "Short Calculus: The Original Edition of A First Course in Calculus," by Serge Lang. It says, " The derivative of a^x is a^x (log a)." But everything else I look at says the derivative of a^x is a^x (ln a). Since ln a and log a are...
  22. H

    How do you evaluate this log equation?

    Homework Statement log39 + log41/64 + log51 Homework Equations none The Attempt at a Solution I tried answering it by... (3x=9) + (4x=1/64) + (5x=1) because of this, I got 5. Is that correct?
  23. T

    Transforming Log & Exponential Equations

    Write the following log equations as exponential equations and vice-versa. 1.) ln 0.5 = - 0.6931 Differentiate with respect to x. 2.) y = e^x(sin x + cos x)
  24. T

    Transforming Log & Exp Equations: Differentiate wrt x

    Write the following log equations as exponential equations and vice-versa. 1.) ln 0.5 = - 0.6931 Differentiate with respect to x. 2.) y = e^x(sin x + cos x)
  25. S

    Uncertainty with a log function

    Homework Statement Im trying to find the uncertainty for a log function. I have that f = 20log(V_in/V_out) and i want to know (delta)f Homework Equations f = 20log(V_in/V_out) The Attempt at a Solution I was going to do it the calculus way: f = 20log(V_in) -20log(V_out)...
  26. W

    Limit of (1-2/n)^n as n --> Infinity

    Homework Statement Find the limit as n--> infinity of (1-2/n)^n Homework Equations We know (1+1/x)^x --> e as n--> infinity The Attempt at a Solution I worked it out as e^(-2) using log but I can't get it out using the fundamental limit above. I know it's the square of (1-1/x)^x...
  27. K

    Behavior of the natural log at large values of x

    Hello, I am fairly new here, so thank you in advance for your help. This is not a homework problem, just one of curiosity based on my limited knowledge of asymptotic expansions. I'm curious about how the function ln(x) or ln(1+x) behaves for large values of x. Plotting in Matlab, I see a linear...
  28. ShayanJ

    The derivative of log and exp functions

    Hi I want to know is it possible to differentiate exp and log functions where bases are functions not constants?How? Thanks
  29. Hepth

    Solving Tough Integral with Log - Need Help

    I posted this in the mathematical/computation software forum but maybe there's an algebraic trick I don't know to help me solve this. I need to compute an integral of: \sqrt{\text{E1}^2-m^2} Log\left( \frac{m^2-m_B E1-m_B\sqrt{E1^2-m^2}}{m^2-m_B E1+m_B \sqrt{E1^2-m^2}}\right) over the...
  30. Hepth

    Mathematica Mathematica Tough Log Integration

    I have an integration to perform \sqrt{\text{E1}^2-m^2} Log\left( \frac{m^2-m_B E1-m_B\sqrt{E1^2-m^2}}{m^2-m_B E1+m_B \sqrt{E1^2-m^2}}\right) Sqrt[E1^2 - m^2] log((m^2 - mB (Sqrt[E1^2 - m^2] + E1))/( mB (Sqrt[E1^2 - m^2] - E1) + m^2)) over the region {E1,m,mB/2} E1 is the variable. m is...
  31. C

    How do I solve for K in ln(1-4k) = -6k?

    Homework Statement Trying to solve for K: ln(1-4k)=-6k Homework Equations The Attempt at a Solution I know that need to take the e of both side, to get 1-4k=e^-6k, but I cannot remember any properties of e to allow me to remove the k from the exponent. Any tips is appreciated.
  32. H

    Solve Log Problem: n^6 = log_2n(1944) = log_n(486√2)

    Homework Statement If log_{}2n(1944) = log_{}n(486\sqrt{}2) then evaluate n^6 P.S the 2n and n are subscripts. Homework Equations log base b(a) = c is the same as a^c = b The Attempt at a Solution I tried converting log base 2n to log base n but I ended up nowhere.
  33. M

    Bessel Differential Equation With Log

    I am trying to solved a differential equation of Bessel type, X^2 Y('')+XY(')+(X^2-n^2)Y+YlogX=0, where Y(')=d/dx. Please help me that how to deal with such equation.
  34. A

    Log N(s) vs Log S Graph for Radio Galaxies

    Homework Statement if the intrinsic brightness of a class of radio galaxies fades as the universe ages, such that those that we see further away are brighter, having a linear increase in luminosity with distance r, what would be the slope of a graph of log N(s) versus log S for these objects...
  35. F

    Exploring the Log of (n^n)*(x^(n^2)): Why is it 0?

    Homework Statement I want to find the limit as n approaches infinity of (n^n)*(x^(n^2)), and Homework Equations My teacher told us to look at the log. 0<x<1. Also, since the log of this goes to -infinity, then the original limit in question goes to 0. (1) why is looking at log valid...
  36. L

    Solving Log Problems: 2 Quick Challenges

    I'm new here. You already knew that. Thank you, you, for clicking on my thread in any case. So, I've got these two log problems. My math teacher gave them out as a challenge. The class is relatively new to logs, and I'm having trouble working with these longer questions (longer than "simplify...
  37. J

    How are we able to take the log of both sides of the equation?

    Here is an equation: x^3 + 1 = 3^x We have no problem of taking ln of both sides, right? But if we write the equation as x^3 - 3^x + 1 = 0 Now let's take ln of both sides ln ( x^3 - 3^x + 1 ) = ln (0) But ln (0) is undefined. My question is: After just taking 3x to the...
  38. E

    How do I solve this natural log integration problem?

    Homework Statement \int^{4}_{2} \frac{dx}{x\left(lnx\right)^{2}} Homework Equations Let u=lnx du=\frac{1}{x}dx x=2 \rightarrow u=ln2 x=4 \rightarrow u=ln4 The Attempt at a Solution so with the u substitution we have: \int^{ln4}_{ln2} \frac{1}{u^{2}}du which goes to...
  39. J

    Solving for x: log 3 (x^2 -5x+6) - log 2 (2-x) = 2

    Homework Statement Find x: log 3 (x^2 -5x+6) - log 2 (2-x) = 2 Homework Equations The Attempt at a Solution I tried and got: (3-x).[(2-x)^1-log 2 (3)] = 9 but I don't know how to get x here ...
  40. S

    How Do You Solve Logarithmic Equations Involving Quadratics?

    Q: Logx = 1 + 6/logx my attempt so far: Log x^2 = 7 where do i go from here?
  41. M

    Solving Log Equations (Different Bases)

    Homework Statement Only the equation: 2(3^x) = 7(5^x) Homework Equations N/A The Attempt at a Solution Okay. I've been fine learning the loglaws, until I hit this question. If they were the same base (or at least near the same, ex: 2 & 8) then I could simply change them into...
  42. J

    Separable ODE, should I take the log of both sides?

    Homework Statement Solve dy/dx = exp(x-y) given that y = ln 2 at x = 0Homework Equations None.The Attempt at a Solution Firstly let's get the equation into a form so we can re-arrange the x's and y's, and then re-arrange. dy/dx = exp(x)/exp(y) exp(y)*dy = exp(x)*dx Integrate: exp(y) =...
  43. C

    How do I solve for x in this log equation?

    Homework Statement 0.5log(2x-1)+log\sqrt{x-9}=1 Homework Equations N/A The Attempt at a Solution I have no idea how to approach this.
  44. C

    How do I evaluate this log expression?

    Homework Statement 5^(log510-1) Homework Equations n/a The Attempt at a Solution I have no idea how to approach this.
  45. J

    Numerical solution to equations with log?

    Homework Statement Merry Xmas~ I hope there's still someone online during the holiday season. I'm trying to solve a set of static laser rate equations but with log in the expression. I think, there's no analytic solution but I don't really know how solve the problem numerically with Matlab...
  46. S

    Math: log question-solving for x.

    Homework Statement Solve: log(sub6)x+log(sub6)(x-5) = 2 Homework Equations na? The Attempt at a Solution i multiplied the second log out and got: log(sub6)x+log(sub6)x-log(sub6)5 = 2 then i put the x's on one side and the numbers on the other. 2(log(sub6)x) = 2+log(sub6)5...
  47. I

    Solving Complex Log Derivatives: y = log_2(x^2+1)

    Homework Statement y = \log_{2}(x^2 + 1) Homework Equations I think the pattern is: \frac{d}{dx}[\log_{b}(x)] = \frac{1}{x ln(b)}The Attempt at a Solution y\prime = \frac{2x}{(x^2+1)ln(2)} I did this by applying the pattern (that may or may not be correct) and then chain ruling the...
  48. N

    Gaussian curve, x is a log scale

    Hello! If I have the gaussian function, but x is a loarithmic scale. Can I infer that, if x was plotted using a regualr scale, that the function would be 'fairly' linear? At least initially? As the rate of change gradually increases befor slowing down again. I think this is reasonable... I...
  49. W

    How to Solve the Equation log(4x) = 1 + log(2, 2x)?

    Solve the equation log4x=1+log22x, x>0
  50. Y

    Solving equation with natural log with inverse hyperbolic

    Homework Statement Solve ln(sinh-1(x)) = 1 (Just give the formula for x, no calculator is necessary) sinh-1(x) = asinh Homework Equations The Attempt at a Solution When I did this, I knew sinh-1(x) = ln(x + sqrt.(x^2 +1), but the equation would look like ln(ln(x +...
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