# [Logarithms]Kepler's third law of planetary motion

1. Dec 7, 2011

### anonymous12

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

Rewrite the formula as a single logarithm.

2. Relevant equations
$$log P = \frac{1}{2} (log K + 3log R)$$

3. 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.

2. Dec 7, 2011

### anonymous12

Nevermind. I got it!

3. Dec 7, 2011