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Log in a diagram

  1. Feb 24, 2009 #1
    1. The problem statement, all variables and given/known data

    http://img21.imageshack.us/img21/2327/nummer1.jpg [Broken]

    2. Relevant equations

    6(a) y=2 so the answer should about 3,3

    3. The attempt at a solution
    6(b)
    Proplem is that i dont know what the opposite(invert) of log3 is...
    then i could take that opposite and use it on y... a litle help here please :-)
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Feb 24, 2009 #2

    Tom Mattson

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    The inverse of a logarithmic function is an exponential function. That is, let [itex]a>0[/itex], [itex]a\neq 1[/itex]. Then if [itex]f(x)=log_a(x)[/itex] then [itex]f^{-1}(x)=a^x[/itex].

    Does that help?
     
  4. Feb 24, 2009 #3
    no (sorry), i think i was wrong, and i am utterly and completly lost... would apreciate a litle help to get back on track...
     
  5. Feb 24, 2009 #4

    Tom Mattson

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    OK, try this.

    1.) Write down [itex]y[/itex] as a function of [itex]x[/itex]. You should be able to do this using part (b) of the given information. Call this function [itex]f(x)[/itex] for now.

    2.) Note that [itex]y=\log_3(z)[/itex], as stated in the problem.

    Since [itex]y=f(x)[/itex] and [itex]y=\log_3(z)[/itex] what can you conclude about [itex]z[/itex] as a function of [itex]x[/itex]?
     
  6. Feb 24, 2009 #5
    well, if y is a function of z then f(x) must also be function of z

    so, f-1(x)--> z=log3(y)? hmm...
     
  7. Feb 24, 2009 #6
    wait, f(z)=x?
     
  8. Feb 24, 2009 #7

    Tom Mattson

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    No, [itex]y=f(x)[/itex]. [itex]z[/itex] is some other function of [itex]x[/itex] (call it [itex]g(x)[/itex]. But first thing's first: You need to find [itex]y=f(x)[/itex]. It should be easy--its graph is a straight line!
     
  9. Feb 24, 2009 #8
    first i have to remove the log, that is to put it into y side of the equation. agh, sorry. It's the midle of the night were i am sitting rigth now, so i am strugeling a bit.
     
  10. Feb 24, 2009 #9

    Tom Mattson

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    :confused:

    Forget the log for a minute. I'm asking you to find [itex]y[/itex] as a function of [itex]x[/itex]. They gave you the slope of the line and a point that the line passes through. Do you know how to write down the equation of a line?
     
  11. Feb 24, 2009 #10
    what is a gradient? (it is the midle of the nigth here...)
     
  12. Feb 24, 2009 #11

    Tom Mattson

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    gradient=slope
     
  13. Feb 24, 2009 #12
    errr, y=ax+b? and, ohh, i remember gradient is the slope of line wich is a. so in this case y=2x+b?
     
  14. Feb 24, 2009 #13
    then 5/9=2x+b?
     
  15. Feb 24, 2009 #14

    Tom Mattson

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    Yes.

    No. You need to use the given point on the line to find b.
     
  16. Feb 24, 2009 #15
    fot that point, that is...
     
  17. Feb 24, 2009 #16
    so i have to make quess on what x is in this given case? wich would be 2,3...
     
  18. Feb 24, 2009 #17
    wich would make b=-4.04444...
     
  19. Feb 24, 2009 #18
    to sum up; the answer should be z=2*2.3-4.0444...
    Is this wrong? somebdy please check this answer! :-)
     
  20. Feb 25, 2009 #19

    Tom Mattson

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    hostergrad, if you don't know how to write down the equation of a line given the slope and a point then this whole enterprise is pretty hopeless.

    No, for any point on the line. A slope and a point uniquely determines a straight line.

    No, they gave you the coordinates of a point on the line:

    [tex](x,y)=\left(1,log_3\left(\frac{5}{9}\right)\right)[/tex]

    No, and I have no idea of how you arrived at that.

    It's wrong. We can continue once you give me the equation of that line. I'm not going to respond to any more random guessing.
     
  21. Feb 26, 2009 #20
    ohh, wait. I wass up 2'o clock in hte night doing this and i somehow tough 1=y. really, staying up that late melts my brain... but what can i do? I live in eroupe and that's the only time the american conticent are awake (aviable at the computer, that is)...
    ok so we get the equation:

    y=2(1)+b

    then; b is the y intercept.

    so the y inercept would be z-2 (the 2 is the slope) or (5/9)-2?
    that would mean that b=-13/9
    wich gives us that:

    z=2x-(13/9)=5/9

    but that being said, im still not sure that i found b the rigth way. So migth not correct either...
    Sorry for being stupid:frown: , but at least i am trying to understand it... tougth i can understand that it is frustrating when i seem completly unable to grasb this. Yes, my ability to remember math formula is a bit bad... thats why i'm here, because i dont have the people skils to get classmates to help me...:confused: but I do really apreciate the help!:approve:
     
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