What is Logarithmic: Definition and 362 Discussions

A logarithmic scale (or log scale) is a way of displaying numerical data over a very wide range of values in a compact way—typically the largest numbers in the data are hundreds or even thousands of times larger than the smallest numbers. Such a scale is nonlinear: the numbers 10 and 20, and 60 and 70, are not the same distance apart on a log scale. Rather, the numbers 10 and 100, and 60 and 600 are equally spaced. Thus moving a unit of distance along the scale means the number has been multiplied by 10 (or some other fixed factor). Often exponential growth curves are displayed on a log scale, otherwise they would increase too quickly to fit within a small graph. Another way to think about it is that the number of digits of the data grows at a constant rate. For example, the numbers 10, 100, 1000, and 10000 are equally spaced on a log scale, because their numbers of digits is going up by 1 each time: 2, 3, 4, and 5 digits. In this way, adding two digits multiplies the quantity measured on the log scale by a factor of 100.

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  1. D

    Calculating a deriv using logarithmic differentiation

    Hello,This is my first crack at using log differentiation, but I can't seem to get too far with it... Use logarithmic differentiation to calculate the derivative for the following function: y = \sqrt{x}e^{x^{2}} (x^{2} + 1)^{10} lny = \frac{1}{2}lnx * x^{2}lne * 10ln(x^{2} + 1)...
  2. D

    Solving Complex Logarithmic Equations

    Homework Statement ln(6xy)-3ln(2y)-1/3 ln x + ln 20 The attempt at a solution I can get to ln\left(\frac{120xy}{8y^3x^1^/^3}\right) And then to ln\left(\frac{120}{8}*\frac{x}{x^1^/^3}*\frac{y}{y^3}\right) But then I am supposed to do something to get to...
  3. S

    Real World EXAMPLES of Exponential and Logarithmic Functions

    Hey, is there anyone who can provide 2 graphical examples of either logarithmic or exponential functions relating to the real world. I've looked in many places and have given up. Please help. Thanks in advance
  4. N

    Logarithmic p-Series: MathCad Findings

    Homework Statement According to textbooks, the logarithmic p-series given by [tex]\sum_{n=2}^n \frac{1}{n \ ln(n)^p } [\tex] and should converge when p>1 and diverge when [tex]p \leq 1 [\tex] Homework Equations Using MathCad (version 11 to 14), I find that the corresponding integral...
  5. R

    Using logarithmic differentiation

    using logarithmic differentiation I can get it to a point where I have... ln(y)=20[ln(x+sqrt(x))-ln(x^2-2^x)] I do not know what to do at that point
  6. M

    Sound intensity is measured on a logarithmic scale

    Help please! Here is the prob and i don't not know where or how to begin. 1.Jose was having a really bad day out on the bike. He should have checked the forecast. First, the wind coming out of nowhere. Must have been a steady 30 mph with gusts up to 50, head on. Then the lightning. First 1...
  7. C

    How Can You Simplify Logarithmic Expressions Using the Change of Base Formula?

    this is what I'm having trouble with: Let r = log6 17, s = log4 17, t = log6 4. Write the following expressions in terms of r, s, and/or t. The change of base formula may be helpful in finding some of these logarithms. log16 17 =...
  8. X

    Master Logarithmic Functions with Our Homework Statement - [Insert Company Name]

    Homework Statement http://img66.imageshack.us/img66/811/untitled1fk8.th.jpg I have no idea what to do, can someone point me in the right direction?
  9. S

    Logarithmic Series Expansion Using Taylor's/McLaurin's

    Hi there guys. My first post here. I heard this forum was really helpful so I've signed up lol.I'm trying to get to grips with using Taylor's/McLaurin's formula for series expansions...My main problem lies with expansions of Logarithmic functions.. I want to work out how to expand Logs when...
  10. G

    How intense is an earthquake of magnitude 5 compared to magnitude 3?

    How many times more intense is the ground movement of an earthquake of magnitude 5 as compared with a magnitude of 3? Using M = log A. Ted
  11. H

    Proving Logarithmic Rule: log_a(x^k)=klog_ax

    prove: log_a(x^k)=klog_ax i can do the addition and subtraction rules no problem, but for some reason I'm stuggling with this one, just point me in the right direction, or help with the whole thing I'm not bothered, i just hope it aint in my exam tomorrow lol
  12. M

    Find Coefficient of x^n in log e (a+bx+cx^2)

    Find the coefficient of x to the power n in the expansion of log e ( a + bx + cx2 ) where a,b,c,n belong to R. (Note: cx2 means it is c x (X square ) and e is base for which the above logarithm is defined.)
  13. WolfOfTheSteps

    Logarithmic Plotting for Function of Temperature

    Homework Statement I have a function of temperature, and I am asked to do the following: "Plot it in logarithmic scale as a function of the logarithm of temperature" The Attempt at a Solution Does this mean I just make the horizontal axis, T, a logarithmic numberline? Or do I have to...
  14. N

    Logarithmic Problem: Is There an Error?

    I an somewhat a layman, but i came across this problem. For any a & b, (b is not 0): ¤ a/b - a/b =0. [taking log to base 10 both sides] ¤ log(a/b - a/b) = log0. ¤ Log((a-a)/b) = log0. ¤Log(a-a) - logb = log0 ¤ log0 - logb = log0 ¤ -logb = log0-log0 ¤...
  15. C

    Solving a Logarithmic Equation: Log(5) X = 1/2Log(5) 25

    Homework Statement solve:Log(subscript 5) X = 1/2log(subscript 5) 25 Homework Equations [b]3. The Attempt at a Solution [/ Log(subscript 5) X = 1/2log(subscript 5) 25 --------------- --------------------- Log(subscript 5) Log(subscript 5) Then they cancel out...
  16. T

    Is My Logarithmic Differentiation Method Correct?

    Homework Statement http://img253.imageshack.us/img253/5748/logdiffji4.jpg The Attempt at a Solution I've tried both and i) and ii) however something just doesn't seem right. Can somebody tell me if my method is correct? i) http://img253.imageshack.us/img253/8791/img0186anh3.jpg...
  17. I

    Logarithmic into exponential form

    Homework Statement Write this logarithmic form into exponential form Homework Equations N = 0.2 Log4 V The Attempt at a Solution I tried V/0.2 = 4^N doesnt seem to work. I've tried doing various inverse functions but that doesn't seem to work either, giving me a headack :(
  18. W

    Switching between exponential and logarithmic form

    Hello you bunch of owls, I'm doing my homework at the moment and I'm curious, how woul I express the logarithmic equation f(x) = log5 (x) + 3 in it's exponential form (where 5 is the base). This isn't part of the homework, I'm just supposed to graph it, but I'm curious as to what the...
  19. T

    Exploring Logarithmic Laws: When x Has Dimensions

    Say you have the function f(x)=log(x). If x had dimensions of metres, say, then you can't have x=2m or whatever because dimensions can't be put into the equation to give log(2m). What about if you have x1=4m and x2=2m and put log(4m)-log(2m) Each term doesn't exist by itself, but using...
  20. E

    Is My Logarithm Solution Correct?

    Homework Statement I got this problem in an exam today, and I think I may have the right answer but I don't understand how I'm supposed to know if I do. It's very confusing. Homework Equations If logb (9) = 1.5 and logb (2) = 0.5 what is logb (5throot(36))? The Attempt at a Solution...
  21. E

    Solve Logarithmic Equation: 3 Solutions Explained

    Homework Statement I'm trying to solve this logarithmic equation, which has 3 possible solutions. However, I can only get to one of them. What are other ways I can solve it so I get to these other solutions? Homework Equations (ln x)^3 = 3 ln x The Attempt at a Solution (ln x)^3 =...
  22. J

    Finding the Value of "e": Exploring the Logarithmic Function

    hey i know what the log function is log a (x) : can be translated to : a ^ y = x with y to find but with the Ln its ln(x) = e ^ y = x with y to find and e = about 2.7... But why this number ? whats special about 2.7... ? whats the exact value of e ?
  23. A

    Solving Logarithmic Equations: Find log[base 2]log[base 3]a = 2

    I have a question I need to do which I'm stuck on: find a log[base 2](log[base 3]a) = 2 How would I do that? And sorry about the crude representation of the base, but I'm not sure how to do a small 2 or 3 on the computer. Edit: oh damn, wrong forum. I guess it has to be moved to the...
  24. H

    Logarithmic differentiation

    1. ln x^(1/5) = 1/5 ln x which = 1/5 *1/x so overall it = 1/5x correct?? Iam so lost on this problem. 2. F(y) = y ln (1 + e^y) any help would be appreciated
  25. B

    Logarithmic Equations: Solving for log2^5 and loga^20 in terms of x and y

    If loga^2=x and loga^5=y, find in terms of x and y, expressions for a) log2^5 b) loga^20 so loga^2 = ____log^2_____ log^a so log^2 = x * log^a Iam not sure where to take it from here or whether I am even going down the right route any help/ideas welcome
  26. L

    Solving a Logarithmic Chain Rule Problem with u(r) Differentiation

    Problem: u(x) = u_1(x)u_2(x)\cdot\cdot\cdot u_n(x) Show that u'(x) = u(x)\left[\frac{u'_1(x)}{u_1(x)} + \frac{u'_2(x)}{u_2(x)} + ... + \frac{u'_n(x)}{u_n(x)}\right] Hint: Take the logarithm of u(x) first. I solved this by using the chain rule. Regarding the hint, am I missing...
  27. A

    Logarithmic Graphs in Graphmatica

    I am trying to scale the y-axis as follows: 0.1 0.4 0.8 1.6 3.2 6.4 12.8 25.6 51.2 102.4 204.8 406.9 819.2 I want the major units to double with each step up the y-axis, starting at 0.1 and terminating at 819.2. The problem is, I have no idea how to achieve...
  28. H

    How Do You Solve the Equation log(x) = sqrt(log(x))?

    Hello, I'm having trouble recovering all the solutions for this equation; here is the work I've managed to produce thus far. logx=\sqrt{logx} (logx)^2=logx 10^logx^2=x <--I'm not sure of this move? x^2=x x^2-x=0 x(x-1)=0 x= 1, 0 I know 0 cannot work, and 10...
  29. N

    Differentiating Logarithmic and Exponential Functions

    a question i couldn't get the right answer to: Differentiate 1. y= 3^x (log(3) x) [3 = base (dont know the right syntax for typing up logs on the web)] what i have so far: y = 3^x (ln 3) (log(3) x) + 3^x / xln3 right...
  30. D

    Summation of 1/p: Logarithmic Growth of N

    \sum_{p\leq N}\frac{1}{p}=\log\log N + A + O(\frac{1}{\log N}) Does it mean that we can simply replace the O part with a function that is a constant times 1/(log N)? What would be the difference between A + O(\frac{1}{\log N}) and O(1)?
  31. F

    Exponential and logarithmic properties

    Hi. I'm having trouble solving for t: 1180 = 98t + 1080e^(-t/10) I know basic properties but I think I am not remembering some idea or specific property to be able to solve this. Thank you for any help.
  32. H

    How can Pete solve a logarithmic problem using the Change of Base Formula?

    Pete has access to a scientific calculator and only knows the Definition of a Logarithm and the Change of Base Formula. How is Pete able to solve the following problem?: x^(log base x of y) =
  33. Q

    Exploring Series and Logarithmic Functions

    Just a few things that I've been thinking about lately: Are there any taylor/power series that converge to logarithmic functions (f(x)=log(x), etc.)? How would you do this? Is there any series that will graph the traditional bell curve? How would you do this? I remember the derivation...
  34. W

    Proove logarithmic differentiation by induction

    {\frac{P'(z)}{P(z)} = \frac{1}{z-z_1} + \frac{1}{z-z_2} + . . . + \frac{1}{z-z_n} where P(z)=(z-z_1)(z-z_2)...(z-z_n) Any hints? I've shown it works for a few specific cases..now I have to show that it works for n=k+1. I tried adding a \frac{1}{z-z_{k+1}} term to both sides, and trying the...
  35. V

    Derivatives of Exponential and Logarithmic

    Hi, I'm having a little bit of difficulty surrounding three problems I've been working on. All fall within the logarithmic/exponential derivative/limit category... 1.) http://www.synthdriven.com/images/deletable/calc01.jpg The problem I'm having here is with what happens to -sinx to...
  36. R

    Understanding Logarithmic Properties: Explained with Examples

    Okay i did a search for logarithmic properties and logarithms and couldn't seem to find an explanation for how this particular property works. (log base c of a ) ^ b = b (log base c of a) when i input simple numbers like : a=4 b=3 c=2 Log base 2 of 4 obvioussly the answer is 2, but 2^3...
  37. R

    Can Someone Explain This Logarithmic Property Discrepancy?

    sorry this should go under the " Homework, Coursework, & Textbook Questions" forum. please delete. i will repost. Okay i did a search for logarithmic properties and logarithms and couldn't seem to find an explanation for how this particular property works. (log base c of a ) ^ b = b (log base...
  38. A

    Inverse Logarithmic Differentiation

    Hey everyone, I'm having some trouble with a couple HW questions. A little help would be greatly appreciated. 1. Find the derivative of: y=2(arcsin(x^2)) I thought you had to make a u-substition of u=x^2, but it doesn't seem to work out. If anyone could point me in the right direction that...
  39. X

    Natural logarithmic function problem

    This is the problem: (A) By comparing areas, show that \frac{1}{3}\ll\ln1.5\ll\frac{5}{12} (B) Use the Midpoint Rule with n=10 to esimate \ln1.5.I've seen these types of "comparing areas" problems but I kind of forgot how to go about solving the problem...I was thinking...
  40. L

    What is the issue with log scales and plotting values less than 1?

    I am working on a homework for a programming class. We have to create a Logarithmic plot and add to it a marker when the program is running on the click of the mouse. That is NOT the problem :) , in fact, that's very simple! My problem, however, is with the scale. When my plot is in linear...
  41. N

    Exponential equation vs Logarithmic

    Hi I was wondering what is the relationship between y=a^x for exponential and y=loga (x) for log I koe that we can divided this questiong further such as a) equations --- which I am not sure b) Graphs - I think we can say that the graph of the log equation is the reflection of...
  42. A

    Calculus Solving logarithmic equations

    If (log x)^2 + log x^3 - 27 = log x^4 - log x^7, solve for x to 2 decimal places (log x)^2 + log x^5 - 27 = log x^4 - log x^7 (log x)^2 + 6 log x - 27 = 0 Let log x be a a^2 + 6a - 27 = 0 (a + 9)(a - 3) = 0 a = 3 or - 9 log x = 3 or log x = -9 ... x = 10^3 or 10^-9 Please...
  43. M

    Logarithmic Function with Vertical Asymtote at X=-6, Y Intercept=5

    what will be the logarithmic function with a vertical asymtote at X = -6 that has the intercept Y = 5 I know the denominator will be x+6 to get vertical asymtote, but don't know how to get Log Function ??
  44. B

    Logarithmic differentiation to find dy/dx

    Hello, I know how I need to do the problem, I have figured out an answer as best as I could but I have a feeling the answer is not correct. In fact I'm pretty sure it's not. Anyway, I'm supposed to use the logarithmic differentiation to find dy/dx for the equation: x^y = y^x I know I need...
  45. B

    How to write this logarithmic equation as a power

    how can the relationship between y and x in the form Iny = 3+0.2x, be written in the form y = pq^x. I tried many ways, but can't find the righ format, someone help please?
  46. M

    How Can You Efficiently Calculate x from y = log2(x)?

    Hello All, I have a very impotant question for you. Any help is appreciated. Given is a logarithmical function: y = log2x (2 is the base) and the y value is known. I have to find out what is the x value in the fewest steps possible. It can be made by giving sample values for x and...
  47. K

    Details of logarithmic calculations?

    From where I can get the details of lograthmic calculations?How the values are found?and on what basis?
  48. Y

    Solving the Logarithmic Equation: \ln(x)^{\ln(x)} = x^\ln(\ln(x))?

    Is it right that \ln(x)^{\ln(x)} = x^\ln(\ln(x))? If i take ln from both sides it looks ok. but when i try to plot \frac{\ln(x)^{\ln(x)}}{x^\ln(\ln(x))} or \ln(x)^{\ln(x)} - x^\ln(\ln(x))? it doesn't gives me straight line. What is wrong?
  49. F

    .Unraveling the Mystery of 1=2: A Logarithmic Proof

    everybody seems to know at least one of the "proofs" that 1=2 or 1=-1, etc but i had never seen this one before. check it out: everybody knows that log(1+x) = x-\frac{x^2}{2} + \frac{x^3}{3} - ... plug in x=1 & the series converges & we get log2 = 1 - 1/2 + 1/3 - 1/4 + 1/5 - 1/6 + 1/7 -...
  50. J

    Need help on finding derivatives of logarithmic functions

    These are the problems (Please, just point me in the right direction): y=x^{2}\ln(6x) f(x)=x\ln(12x)
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