[Logarithms]Kepler's third law of planetary motion

AI Thread Summary
Kepler's third law of planetary motion is expressed in the equation log P = (1/2)(log K + 3log R). The formula can be rewritten as a single logarithm: log P = log(K^(1/2) * R^(3/2)). The textbook solution shows that log(K^(1/2) * R^(3/2) / P) = 0, indicating that K^(1/2) * R^(3/2) equals P. The discussion highlights the process of transforming the equation and resolving confusion about the final result. Understanding this relationship is crucial for applying Kepler's law in planetary motion studies.
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Homework Statement


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 log P = \frac{1}{2} (log K + 3log R), where K is a constant.

Rewrite the formula as a single logarithm.

Homework Equations


log P = \frac{1}{2} (log K + 3log R)

The Attempt at a Solution



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

I have no idea what to do next.

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

Here I have no idea how they made the equation equal to 0. If anyone could help me I will be very grateful.
 
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Nevermind. I got it!
 
Glad we could help!
 
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