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Help with logarithms and graphs

  1. Mar 21, 2012 #1
    1. Determine the equation y=f(x) for each of the following cases in simplest form. All of the plots are straight lines and all coordinates are indicated with abscissa first, ordinate second (x,y).

    -log y versus log x on a rectilinear graph passes through (5,7) and (2,3)

    -(y-2)^2 versus x on a log-log graph passes through (1,2) and (3,4)

    -√y versus x on a semi-log graph passes through (3,2) and (6,4)




    2. Relevant Equations

    -Power Equation : y = bx^m

    -Linear Equation: y = mx +b

    -Exponential Equation: y = be^mx or y = b10^mx (e is base 10)

    -Point slope formula: y-y1 = m(x-x1)



    3. For the first problem, I found the slope, m, which is 4/3 (or 1.333) and then I used the point slope formula to get y = 1.333x + 0.35. This equation is in a linear format but the thing that confuses me is the "log y versus log x". I used this same process for the other problems but I'm still confused by the "(y-2)^2 versus x on a log-log graph" and
    √y versus x on a semi-log graph". I really don't understand how to implement that part of the question into the solution, so any help would be appreciated.
     
  2. jcsd
  3. Mar 21, 2012 #2
    Hint:

    On a non-log graph, the coordinates are (10000,10000000) and (100,1000).
     
  4. Mar 22, 2012 #3

    NascentOxygen

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    Staff: Mentor

    Hi shinto1. http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif [Broken]

    I took that to be a minus sign ("–") in front of your log function, and didn't realise it wasn't until I got to the -√y plotted on semi-log paper!

    [PLAIN]https://www.physicsforums.com/Nexus/statusicon/user_online.png [Broken] [Broken] (y-2)^2 versus x on a log-log graph passes through (1,2) and (3,4)

    [PLAIN]https://www.physicsforums.com/Nexus/statusicon/user_online.png [Broken] [Broken] √y versus x on a semi-log graph passes through (3,2) and (6,4)

    Do you understand what LawrenceC wrote about the first graph?

    If a log-log plot is a straight line, then those same points plotted on an ordinary graph (rectilinear) will likewise be a straight line, but much expanded.
     
    Last edited by a moderator: May 5, 2017
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