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Expressing a logarithmic equation

  1. Jun 3, 2009 #1
    1. The problem statement, all variables and given/known data

    http://img142.imageshack.us/img142/8564/76203773.jpg [Broken]


    2. Relevant equations

    I need to somehow express the above equation in terms of logax, logay,and logaz.


    3. The attempt at a solution

    I got the answer loga * [ |x|*sqrt (x)] + loga * [|y|] - loga * [z]

    But I'd just like to get your guys' opinion, because I have the feeling I'm wrong, lol.
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Jun 3, 2009 #2

    rock.freak667

    User Avatar
    Homework Helper

    How'd you get those answers? Did you use these laws?

    [tex]log_a xy= log_a x + log_a y [/tex]

    [tex]log_ax^r=rlog_a x [/tex]

    [tex]log_a \frac{x}{y} = log_a x - log_a y[/tex]
     
  4. Jun 4, 2009 #3

    Mark44

    Staff: Mentor

    And your expression (NOT an equation) can be written as
    [tex]\log_a (\frac{x^3 y^2}{z})^{1/2}[/tex]
    so you can immediately use the second law that rock.freak667 listed, and continue from there.
     
  5. Jun 4, 2009 #4

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Or, not necessary but might help,
    [tex]log_a\left(x^{3/2}yz^{-1/2}\right)[/tex]
     
  6. Jun 4, 2009 #5
    Would http://img23.imageshack.us/img23/7739/97409454.jpg [Broken] be my final answer?
     
    Last edited by a moderator: May 4, 2017
  7. Jun 4, 2009 #6

    Mark44

    Staff: Mentor

    No, for two reasons.
    1. It's wrong. The 1/2 factor should multiply all three terms.
    2. It can be simplified more in the x and y terms.
     
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