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Find log x and log y

  1. Dec 11, 2004 #1
    [tex]\text{Given that } log_b(x^3y)=p \text{ and } log_b(\frac{y}{x^2}) = q \text{ express } log_b(xy) \text{ in terms of p and q.}[/tex]
    [tex]\text{ This is what I've done. } [/tex]
    [tex]log_b(x^3y)=p----(1)[/tex]
    [tex]log_b(\frac{y}{x^2})=q ----(2)[/tex]
    1 - 2
    [tex]5log_bx=p-q[/tex]
    [tex]\text{ I'm stuck here. What do I do next? }[/tex]
     
  2. jcsd
  3. Dec 11, 2004 #2
    Find log x and log y in terms of p and q first
    then split log(xy)
     
  4. Dec 11, 2004 #3
    How do I do that?Could you show me the steps?
     
  5. Dec 11, 2004 #4

    dextercioby

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    [tex] b^{p}=x^{3}y (1);b^{q}=xy^{-2} (2)[/tex]
    (1)=>[tex] b^{2p}=x^{6}y^{2} (3) [/tex]
    (2)*(3)=> [tex]x^{7}=b^{2p+q} (4) [/tex] => log_{b}x=...

    Did u see a pattern??
     
  6. Dec 11, 2004 #5
    Nope. I don't see a pattern. But I figured how to do it. Thanks for help.
     
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