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. A

    Conservation of mass for burning log

    Suppose I burned a log. If I collected all the products of the burning process (the smoke particles, the ashes, etc.) would they have the same exact mass as my original log? Or would they have less mass because they are at a lower energy state then the original log (Energy-mass equivalence)...
  2. D

    When you punch in log on your calculator

    b^x=y log_b(y)=x When you punch in log on your calculator, mathematically, how is it solving for x? For example, 3^x=81 log_3(81)=4 How is this being solved? Thanks
  3. T

    Is log( x^(-y) ) = -y, somebody told me this.

    Can one under any circumstances say that log x^(-y) = -y ?? I'm having some truble with this myself, but someone told me it is so... :confused:
  4. L

    Physics teacher has posted log questions

    My physics teacher has posted log questions (for fun/frustration)almost every day. Having last had logs about 8 years ago, i have no clue how to solve for any of them. And seeing as how we don't actually use them in class, he won't help us figure them out. :bugeye: If anyone can offer me some...
  5. D

    How Do Significant Figures Work in Logarithmic Equations?

    I am rather confused by how the significant figure is suppose to work when you have logarithms in your equation. For example: Francium-87 undergoes beta decay with a half life of 22 min. How much of a 15.00 grams sample remains after 2.0 hours? Well, I used this equation: logA = log...
  6. G

    3 + 2 log (base 2) X = log (base 2) y

    3 + 2 log (base 2) X = log (base 2) y how can this show, that y = 8X squared? Please help! :confused:
  7. Math Is Hard

    C/C++ Predefined log function in C++?

    Is there a predefined function in C++ that will allow me to take LOG(base 10) of a number? If not, is there a reasonably simple work-around? thanks, MIH
  8. C

    Differentiation Question Concerning natural log

    Hello all If y = e^3^\ln^(x^2) find \frac {dy}{dx} So \frac {dy}{dx} =(3 (\frac {1}{x^2}) \* 2x e^3^\ln^(x^2) So the simplified answer is: \frac {6}{x} e^3^\ln^(x^2) Is this correct? IS there any other way of expressing the answer? Thanks
  9. N

    Try solving this log equation using algebra

    6-2x = 3 * log (x) Is it possible to solve such an equation without graphing?
  10. S

    Exploring the Derivative of xlnx with Natural Log

    Hi everyone! (d/dx) [xlnx] Why is the answer 1+lnx and not 1?? ~Thanks
  11. M

    Derivatives of Log and Exponential Functions

    Hi i was wondering if someone could check my work for these couple questions: Find dy/dx (do not simplify) a)y=e^sin3x dy/dx= e^sin3x (cos3x)(3) =3cos3xe^sin3x b)y=5^(square rootx) x^2 dy/dx=x5^(square rootx) (xln5+2) c)y=ln(x^2 / (2x+5)^3 ) y=lnx^2 - ln(2x+5)^3 dy/dx= 2x/x^2 -...
  12. F

    Solve log_b(xy): Express in terms of p, q

    \text{Given that } log_b(x^3y)=p \text{ and } log_b(\frac{y}{x^2}) = q \text{ express } log_b(xy) \text{ in terms of p and q.} \text{ This is what I've done. } log_b(x^3y)=p----(1) log_b(\frac{y}{x^2})=q ----(2) 1 - 2 5log_bx=p-q \text{ I'm stuck here. What do I do next? }
  13. C

    Number Theory Question - Discrete Log mod (pq)^2.

    Hello all, here is a problem I am working on that is giving me some problems. p,q, and N are defined as in RSA i.e. {p,q} in (Z_p,*), N = pq a in (Z_n,*) g in (Z_{N^2}) s.t. g=aN+1 mod N^2 The problem is to show that the discrete log problem base g is easy in Z_{N^2}, i.e. : given...
  14. C

    What are the solutions to ln(z) = 1 and ln(-e^2)?

    Hi there, I was hoping someone could check my solutions here to make sure I'm on the right track with these. We've been asked to find ALL values of z satisfying the following eqts - z= ln(-e^2) which I did by letting ln (-e^2)= ln|-e^2| + iarg(-e^2) = e^2 + i(pi + 2m(pi)) where m = 0...
  15. S

    Log base 4 64 without using a calculator

    i don't understand how to find the exact answer to log base 4 64 without using a calculator. can anyone help?my teacher gave examples but they are on bad photocopies sarah
  16. C

    Strangely difficult log question

    485 + 5 ^ (x + 2) = 12 ^ (2x - 1) This question is driving me nuts. I can't take the log until both sides have been reduced to one expression each, right? If 485 were a power of 5 or 12, then I'd be able to solve it. As it is, I'm clueless. Can someone walk me through the steps to solving for...
  17. D

    Can x be solved in this logarithmic equation?

    Say you have: \frac{\log(x)}{r\log{x}} = y r and y can be any given number. Is there any way to solve this for x? ie \frac{\log(x)}{1.6\log{x}} = 20 I'm getting this because I'm trying to calculate f(x) = \frac{x}{a} where f(x) is of the form f(x) = cx^r a > 1
  18. V

    How Do You Solve ln x + ln(x+1) = 7?

    Can anyone help me with this natural log? ln x + ln(x+1) = 7 I've tried putting it in quadratic form but all I get is x^2 + x - 7=0 which doesn't seem to factor. What am I doing wrong?
  19. A

    Isolating Variable L in G = log [ aL (1-e^(-bL) + S e^(-bL)]

    Hi, I need to isolet the variabl L from the equation, I'll appreciate any help: G = log [ aL (1-e^(-bL) + S e^(-bL)] I know all the other variables and they are all nombers Thanks, Shira :bugeye:
  20. O

    How Do I Solve a Natural Log for x?

    Please Help! Natural Log Question! Here is the question that is bothering me: I need to solve this natural log for x. Please I need step by step instructions on how to figure out x. Thanks very much. ln (x) + ln (x+1) = 2
  21. C

    I'm sorry, I do not understand your comment. Could you please clarify?

    -------------------------------------------------------------------------------- Hello, I need help with this problem: 4^x + 4^-x = 5/2 My Solution: (Assume we use log with base 4) log ( 4^x + 4^-x) = log(5/2) = log (4^0) = log (5/2) ? I don't see what I am doing wrong...
  22. C

    Solving a Simple Log Problem: 4^x + 4^-x = 5/2

    Hello, I need help with this problem: 4^x + 4^-x = 5/2 My Solution: (Assume we use log with base 4) log ( 4^x + 4^-x) = log(5/2) = log (4^0) = log (5/2) ? I don't see what I am doing wrong. I used the Product Rule. Any help would be greatly appreciated. Thanks
  23. F

    Integral problem with natural log ($5 to whoever gets it)

    Here's the problem: find the integral of dx/2x(lnx)^1/2 In other words, dx over 2x times the square root of lnx. It has to be evaluated from 16 and 2. I don't know how to say it, but the integral sign with 16 at the top, and 2 at the bottom. If you can find the answerm and show me...
  24. K

    How Can I Finish Integrating a Natural Log Using Integration by Parts?

    [SOLVED] Integration of a natural log I am asked to Integrate by parts \int \ln(2x+1) dx So, \mbox{u}=ln(2x+1) \mbox{du}=\frac{2}{2x+1} \mbox{dv}=\mbox{dx} \mbox{v}=\mbox{x} I plug all of that in and I get, {\int \ln(2x+1) dx\}={\mbox{x}\ln(2x+1)}-{\int \frac{2x}{2x+1}...
  25. M

    Problem with finding the log function of a graph

    I have a problem where a graph is drawn, and i am supposed to find the function that would create it. We are only given a part of the graph with certain points. They say it is a log function, and the points given are (0, 0.21), (0.5, 0.19), (1, 0.15), (1.5, 0.10), (1.75, 0). It says to choose a...
  26. M

    Decibel Scale and Noise Limits: Understanding Log Problems

    Here is the question as it follows: The decibel scale, defined as L = 10 log (\frac{I}{I_0}) where L is the Loudness (or comparative intensity) in decibels (dB), I_0 is the reference level (10^-12 watts per m^2) I is the actual intensity of the sound measured (watts per m^2)...
  27. S

    Logarithmic Equation: Simplifying with Easy Quick Method

    Does (\log_{x}a - \log_{x}b - \log_{x}c) = \log_{x}(\frac{a}{b/c})?
  28. R

    Understanding the Simplified Equation for 2^-log2(x) and its Relation to x^-1

    2^(-log2(x)) It reads, 2 to the power of -log base2 x The problem is that I don't understand why this can also be written as x^-1 For some reason the base and the log2 cancel out. Can anyone explain to me why this happens, please? 1/2^(log2(x)) = 1/x
  29. W

    Integral of Natural Log Part II

    Hi, I am still having trouble with taking the integral of the following: integral of ln(x+1) dx I am trying to do it by parts but I end up getting stuck. I had no problem doing: integral of ln x dx But I can't seem to get integral of ln (x+1) dx Let u = ln (x+1) then du =...
  30. W

    Integrating Natural Logarithmic Functions

    Hello, It has been over a year since I last took calculus. And I don't recall how to take the integral of a natural logarithmic function. Here is the question that I am supposed to integrate. double integral 1/(x+y) dA where R = [1,2] X [0,1] So what I did first was integrate...
  31. marcus

    Black hole entropy and the log of the golden mean

    there is a curious 1996 paper by Rovelli that gets the black hole entropy/area formula by a simple counting method. I say simple advisedly---a lot of combinatorics and counting is not really simple at all but IMHO difficult---but in this amazing little 5 page paper the counting of...
  32. P

    Chain rule in Calc = Chain in Log?

    I know in Logarithms loga b * logc d = loga d * logc b and loga b * logb c = loga c. Chain Rule. Now I read Calculus, I found out about the Chain rule, are they the same?? Looks like it. But because of my poor English reading, I couldn't understand the text. Can some one explain what...
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