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Homework Help: [Logarithms]Kepler's third law of planetary motion

  1. Dec 7, 2011 #1
    1. The problem statement, all variables and given/known data
    Kepler's third law of planetary motion relates P, the period of a planet's orbit, to R, the planet's mean distance from the sun, through the equation [itex]log P = \frac{1}{2} (log K + 3log R)[/itex], where K is a constant.

    Rewrite the formula as a single logarithm.

    2. Relevant equations
    [tex]log P = \frac{1}{2} (log K + 3log R)[/tex]

    3. The attempt at a solution

    Rewrite the formula as a single logarithm.
    [tex]log P = \frac{1}{2} (log K + 3log R)[/tex]
    [tex]log P = \frac{1}{2} (log(KR^3))[/tex]
    [tex]log P = log K^\frac{1}{2} \cdot R^\frac{3}{2}[/tex]

    I have no idea what to do next.

    4. The answer in the back of the textbook
    [tex]log(\frac{K^{\frac{1}{2}} \cdot R^{\frac{3}{2} }}P)=0[/tex]

    Here I have no idea how they made the equation equal to 0. If anyone could help me I will be very grateful.
  2. jcsd
  3. Dec 7, 2011 #2
    Nevermind. I got it!
  4. Dec 7, 2011 #3


    Staff: Mentor

    Glad we could help!
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