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Simplify natural log ratio

  1. Aug 28, 2008 #1
    how the heck do you simplify this ?????

    (Ln (2x/y) / Ln (x/y)) = m/n

    HELP ME!!!!!!!
     
  2. jcsd
  3. Aug 28, 2008 #2

    marcusl

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    Start by cross-multiplying, then apply what you know about the log of an exponential expression.
     
  4. Aug 28, 2008 #3
    I am just going to elaborate a lill bit what marcusl already suggested.

    You probbably know that

    [tex] log\frac{x}{y}=log(x)-log(y)[/tex]

    Also

    [tex] log(ab)=log(a)+log(b)[/tex]

    just apply these properties, and yu'll be fine.
     
  5. Aug 29, 2008 #4
    Ln (2x/y) = Ln 2x - Ln y

    Ln (x/y) = Ln x - Ln y

    [Ln (2x/y) / Ln (x/y)] = (Ln 2x - Ln y) / (Ln x - Ln y)

    what do I do now?????
     
  6. Aug 29, 2008 #5

    Gib Z

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    Well that wasn't how I interpreted the original hint. After cross-multiplying as already said, to [tex] n \log_e \left( \frac{2x}{y} \right) = m \log_e \left( \frac{x}{y} \right) [/tex], I would have applied the exponential function to both sides and simplified.
     
  7. Aug 29, 2008 #6
    Hell yeah.Gib Z is so right, my bad!
     
  8. Aug 30, 2008 #7
    that's not where I want to go.

    basically, this natural log ratio reduces down to

    1+ (ln 2)/Ln (X/Y)


    how do you get here???
     
  9. Aug 31, 2008 #8

    uart

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    casanova2528, you started with an equation (note the equals sign), so I assume you meant to write : 1+ (ln 2)/Ln (X/Y) = m/n.

    To get this you should use the property of logs that ln(2x/y) = ln(2) + ln(x/y). You should find it pretty easy from there.
     
  10. Aug 31, 2008 #9
    thanks! Those darn properties!
     
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