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. E

    How Do I Solve This Natural Logarithm Problem?

    Homework Statement This is my first time ever posting anything on here...but we just started working with ln? I know that it's the base e? or something like that... but the problem is this... 1/3=ln(x^2/x-4)Homework Equations The Attempt at a Solution I haven't attempted..i...
  2. R

    Resolve Overflow Issue: Log(K) = 127.702 | K = 5.04316 * 10^127

    "If your calculator has overflow issues with this problem, you can use this identity to solve for K: if log(K) = x + y then K = 10x * 10y Problem: log(K) = 127.702 K = 5.04316 * 10127 " Doesn't K = 10127 ? Where are they getting the 5.04316 from? How are they using that specified...
  3. R

    Data weighting on semi log scale

    Hi I have to perform a fitting procedure on a semi logarithmic scale but I'm not sure how to weigh the experimental data points. I'm studying the decay of the luminescence of a certain type of crystals and the function I'm using has the form I = \frac{1}{\tau} e^{-\frac{t}{\tau}}...
  4. J

    Natural log fxn = negative integral?

    Homework Statement True or false? ln(1/10) = -\int dx/x The Attempt at a Solution I have no idea where to start on this one. what is dx/x ??
  5. C

    Derivative of Log Determinant of a Matrix w.r.t a parameter

    Hi, I'm trying to see why the following theorem is true. It concerns the derivative of the log of the determinant of a symmetric matrix. Here's the theorem as stated: For a symmetric matrix A: \frac{d}{dx} ln |A| = Tr[A^{-1} \frac{dA}{dx}] Here's what I have so far, I'm almost at the...
  6. D

    Misc. Can I Use Mineral Oil and Sawdust to Make Fire Logs?

    OK, so paraffin is a hydrocarbon, and is a solid form of kerosene or mineral oil... I wanted to try making my own wax logs for starting our wood stove. Could I take dried out sawdust, mix it with a small amount of mineral oil, suck the moisture out of the "shape", allow for it to dry, then...
  7. Y

    Solve Log Values Problem: Find A and B for \frac{Log A}{Log B} = \frac{2}{3}

    Homework Statement A professor is doing a problem on the black board and ends up with the expression \frac{Log A}{Log B} = \frac{2}{3} . He absentmindedly cancels the “log”, making the left-hand side A/B. (A very wrong thing to do!) Luckily, he ends up with the correct values for A...
  8. N

    How can I use calculus to graph f(x)= 10(ln(ln(x))/ln(x))?

    1. Graphing Carefully: Sketch f(x)= 10(ln(ln(x))/ln(x) accurately using calculus, your calculator, or both to aid you. Make sure to include all vertical asymptotes, as well as local extrema 2. f(x)= 10(ln(ln(x))/ln(x) 3. OK. I might come across as stupid but here goes... I don't...
  9. J

    Calculators TI-89 Titanium date log GPA and Pass or Fail in jeopardy?

    Alrighty, I know the TI-89 keeps up with date and time. It seems logical that it would somewhere inside the chips and silicon it makes a log of the date that data was inputted...rightttt. I made an idiot out of myself and didn't double check my scan-tron after an exam, my professor jokingly said...
  10. G

    How to Calculate the Optimal Jump for a Flea Over a Log?

    I'm given the following problem. A log sits in the woods with a radius "r". Lazy flea wants to jump over the log with the least amount of velocity necessary. If distance "d" away from the center of the log, and angle theta is the angle of velocity above the horizontal. Find theta, d, and v(min)...
  11. S

    Finding log something, in terms of A and B.

    Homework Statement If Logb2=A and Logb49=B, what is logb397, in terms of A and B. This is one of the bonus question in my geometric quiz and i don't remember if the number is 397. I wonder if anyone get this? Homework Equations The Attempt at a Solution here is what i did bA=2 and bB=49...
  12. S

    Finding log something, in terms of A and B.

    Homework Statement If Logb2=A and Logb49=B, what is logb397, in terms of A and B. This is one of the bonus question in my geometric quiz and i don't remember if the number is 397. I wonder if anyone get this? Homework Equations The Attempt at a Solution here is what i did bA=2...
  13. M

    Why is the asymptote shifted and points don't match?

    Here is what the graph looks like on a graphing calculator (notice the equation at the top): http://img62.imageshack.us/img62/8898/graphingcalc.jpg Here is what my graph looks like: http://img53.imageshack.us/img53/7475/lastscanc.jpg I don't understand why the asymptote is...
  14. M

    Understanding Natural Log Problem: Taylor Series Approach

    Homework Statement y and x are both close to 1. ln(y) - ln(x) \approx (y-x)(lnx)' Can someone explain me why this is true? By the way, (lnx)' is the derivative of lnx, which is just 1/x The Attempt at a Solution I guess this is something to do with the taylor series of ln(x). I tried to...
  15. S

    One last log law question. little more trickier.

    Homework Statement 10^{log_{100}4} Evaluate. I'm on a school computer, i cannot see TEX images. Sorry if their not 100% correct. The Attempt at a Solution I solved this answer, and got 2. i did this by making the above equation: 100^\frac{1}{2}(log_{100}4) then using a log law to...
  16. S

    Log Law: Understanding -log_2\frac{1}{9}

    Homework Statement This is not a homework question. Understanding how log_{\frac{1}{2}}\frac{1}{9} = log_2x^2 The Attempt at a Solution Somehow, the base of the first logarith was turned into 2^-1, no problem, but he was able to put the negative up in front of a log to equal...
  17. D

    Convergent/divergent with natural log

    Preparing for the math test, and cannot understand what to do for one of my practice problems: I need to find if the series is convergent or divergent, using test for divergence (divergent if limit doesn't equal 0) sigma from 1 to infinity of ln((n^2+1)/(2n^2+1)) I see that I should use...
  18. P

    Mathematica ParametricPlot and log scale axes in Mathematica

    Hello, I have been trying to make a parametric plot with logarithmic axes in Mathematica, but have been unable to find an option to do this. Can someone tell me how to do this? My code is below, and for reference, EnergyScint[b] is the Bethe-Bloch equation for energy deposit for a fully...
  19. J

    Simple equation involving natural log

    Can anybody solve for x? 6=(36/9)ln(120/x) The answer is x=22.3 I have so far got: 6=4*ln(120)-ln(x) 6=19.15-ln(x) I think it may be incorrect
  20. tony873004

    LOG Base: 10, e, or Other - What Does it Mean?

    If I see a formula that contains LOG, but does not specify as base, how do I know what base they're referring to? Programming languages assume LOG means base e. My calculator assumes LOG means base 10. I've seen math teachers assume it meant base e. If its base anything other than 10 or e...
  21. N

    Mastering the Basics of Natural Logarithms: Simple Proof of ln(e)=1

    Homework Statement Guys how come ln(e)=1 ? How can l prove this
  22. M

    Expressing the Solution of 2^(2x+3) = 2^(x+1) + 3 as a + log2b: Complex Numbers

    Homework Statement The solution of 2^(2x+3) = 2^(x+1) + 3 can be expressed in the form of: a + log2b where a, b belong to the set of complex numbers. The Attempt at a Solution (2^3)(2^x)^2 = 2^(x+1) + 3 [8((2^x)^2)] - [2(2^x)] - 3 = 0 Solving the above quadratic for 2^x, I...
  23. P

    When do you use In or log in Integrals?

    1.For example a.http://img40.imageshack.us/img40/9514/problem2m.png b.http://img193.imageshack.us/img193/4250/problem2ans.png When do you use ln in integrals?
  24. S

    How Do You Calculate Error in Logarithms?

    hi i want to knw the formula to find error in log for example they give me a value of 2.6 +or- 0.1 now they say log this value and give the error i log it and i get 1.176 ok but now how to find the error in log i knw there is a forumla but i forget it
  25. I

    Sum of series involving natural log

    Homework Statement Find the sum of the series, if it converges, of n=1 to infinity of ln(n/(n+1)) The Attempt at a Solution My intuition tells me the series converges because as n goes to infinity the series is taking the log of 1, which is 0. How to sum it though... I have no...
  26. J

    How to Simplify Logarithmic Equations?

    i need help with the following quesitons; a) log_3 27x^2 b) ln (x^2 / y^2) c) ln (xe^x) d) log (2x + 3y) i don't mind if you could direct me in the right direction and i will do my best to go from there :) USING THE RULES FOR LOGS, SPLIT THE FOLLOWING UP INTO SEPERATE...
  27. J

    Easier Way to Simplify log_3 3x?

    hey guys, i have a question, then i will show my solution, is there any chance you guys could help me find an easier way to get to the answer, cheers question: log_3 3x answer: log_a (yx) = log_a (y) + log_a (x) log_3 (3) + log_3 (x) log_a (y) = x -> y = a^x -> log_a (a) = 1...
  28. T

    Big-O With Change of Base for Log

    Homework Statement Hi, I am trying to prove for a>1, b>1 that f(x) = O(log_b(x)) then f(x) = O(log_a(x)). [Hint: log_b(x) = log_a(x)/log_a(b)). Homework Equations The Attempt at a Solution Assuming |f(x)| <= C|log_b(x)| true for x>k, then, f(x) <= log_a(x)/log_a(b)| for all x>1...
  29. B

    Logarithm Rules Proof: Calculus Approach

    proof for the differential log rule proof for the integral log rule please and thankyou
  30. D

    Converting Error in Log2 Form for Arbitrary Base

    Hi, I am trying to represent my data in log2 form rather than "fold change" and I am embarrassed to say I can't remember how convert the error. For example, I have x=3.96 (mean), deltax=0.28 (standard dev). Thus, log2(x)=0.598. But how do I convert the error?? I know how to do it for...
  31. S

    Unraveling the Meaning of '+' Above Log: An Equivalent Expression?

    http://img205.imageshack.us/img205/6923/logp.png What is the meaning of '+' above log? Is there an equivalent expression for this? Thanks
  32. A

    Integration by Parts Problem (Natural Log)

    Homework Statement [Intgrl]ln(x^(2)+4)dxHomework Equations [Intgrl]udv=uv-[Intgrl]vduThe Attempt at a Solution [Intgrl]ln(x^(2)+4)dx, u=ln(x^(2)+4), du=(2x/x^(2)+4), dv=dx, v=x xln(x^(2)+4)-[Intgrl](2x^(2)/(x^(2)+4))dx
  33. T

    Solving log_4(5-x)-log_4(3-x) = 2: Step-by-Step Guide

    Homework Statement log_4(5-x)-log_4(3-x) = 2 The Attempt at a Solution log_4(5-x)-log_4(3-x) = 2 log_4\frac{3-x}{5-x} = 2 where do I go from here?
  34. S

    Solve for z: 2.3(1.2)^5z = 3(4.1)^z

    Homework Statement 2.3(1.2)^5z = 3(4.1)^z solve for z Homework Equations the properties of logarithm The Attempt at a Solution okay I first divided the 3 with 2.3 and got 1.304 then i brough the 5z and the z down which gives me 5z log(1.2)=1.304 z log(4.1) then i plugged log of 1.2...
  35. J

    Solve Log EQ: log3^(2x-9)-2xlog3=-2

    Homework Statement Solve: log3^(2x-9)-2log3^x=-2 Homework Equations None The Attempt at a Solution I am confused with one part of this equation. With the 2log3^x, can you move the x to the front to make it 2x log3?
  36. S

    How do you find the Natural Log of a Number?

    Title says all.
  37. R

    Making a 433MHz Phase Detector with Log Amplifiers

    My group had a design based on the http://www.analog.com/en/rfif-components/log-ampsdetectors/ad8302/products/product.html" which was going to do our task of phase detection by use of what I can best tell was just some log amplifiers and . Well the AD8302 is a TSSOP package and I cannot...
  38. P

    Is nlogn the Same as n Multiplied by logn?

    Hey, Is nlogn (or more specifically nlog[base2]n) the same as: n multiplied by logn? Thanks
  39. K

    Limit Log Rule Help: Find Limit as p->infinity

    Homework Statement Limit as p->infinity of ((p^2-p+1)/((P+1)^2)^(2p+3) In case the parenthesis are confusing, its one giant fraction all raised to the (2p+3) power. 2. The attempt at a solution I set the entire problem equal to L and took the ln of both sides. This let's me move the...
  40. H

    Login Diagram Homework: Solving Logarithmic Equations

    Homework Statement http://img21.imageshack.us/img21/2327/nummer1.jpg Homework Equations 6(a) y=2 so the answer should about 3,3 The Attempt at a Solution 6(b) Proplem is that i don't know what the opposite(invert) of log3 is... then i could take that opposite and use it on...
  41. V

    Derivative of Log3*arccsc2^x: Solving for dy/dx

    Homework Statement find dy/dx of log3*arccsc2^x The Attempt at a Solution I got up to 1/ln3csc2^x * 1/2^x(sqrt(2^2x-1) However there's also a 2^x*ln2 after that How is that? In otherwords how would I derive 2^x would i treat it like e^x or something? Also if its x^x why would that be 1+lnx?
  42. H

    Solving Logarithmic Equation with TI-89 Titanium: Step-by-Step Guide

    Homework Statement http://img205.imageshack.us/img205/2327/nummer1.jpg Homework Equations If you use ti-89 titanium, you write log with base(b) (c=number) as log(c,b) fx; the log of 3x in base 5 is written log(3x,5) (log5(3x))took me forever to figure out The Attempt at a Solution I...
  43. L

    Solve Derivative: log 5^xsinhx

    Homework Statement find f '(x) of 5^xsinhx Homework Equations i feel like I am missing somthing can someone direct me to the right direction pleasee? The Attempt at a Solution product rule (f ')(g)+(f)(g ') f=5^x g=sinhx 5^xsinhx= e^ln(5)^xsinhx...
  44. N

    Horizontal Distance Between Log & Bridge | Homework Statement

    Homework Statement A log is floating on swiftly moving water. A stone is dropped from rest from a 75-m high bridge and lands on the log as it passes under the bridge. If the log moves with a constant speed of 5.0 m/s, what is the horizontal distance between the log and the bridge when the...
  45. E

    Integrating ln(t+1) from 0 to e^2x?

    Homework Statement How would I begin to integrate ln(t+1) from 0 to e^2x? Homework Equations d/dx[log base a of u]=1/(lna)u du/dx Can the original equation be manipulated to use this derivative? The Attempt at a Solution Not sure where to start.
  46. E

    How Do You Solve Logarithmic Expressions Involving Fractions?

    If log_2 (5) = x and log_2 (3) = y , determine an expression for log_2 (15/2), in terms of x and y. A. xy B. x + y C. xy - 1 D. x + y - 1 I'm suppose to solve this by hand but it doesn't seem possible. I tried so many ways but the does not come out as D. which is the answer Can someone...
  47. P

    How to Prove log[(x-y)/3] = 1/2(logx+logy) Equals x^2+y^2=11xy?

    show how log [(x-y)/3]=1/2(logx+logy) is equal to xsquared+ysquared=11xy does anyone know how to solve this. i have tried all kinds of ways though none of them seem to work. any help would be very much appreciated!
  48. P

    How to Solve This Logarithmic Problem?

    show how
  49. P

    How to Solve This Logarithmic Problem?

    show how
  50. C

    Solve Log Equation for x: 2log3x + log3(x-1) = log32 + log36x | Homework Help

    Homework Statement Solve for x: 2log3x + log3(x-1) = log32 + log36x Homework Equations N/A The Attempt at a Solution Ok, so I tried to solve it and I came up with this and got stuck. log3(x3-x2) = log312x Even if I canceled out the logs it would be x3-x2 = 12x and then how would...
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