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 = 1/2 (log k + 3 log R), where k is a constant.

Question

a) Rewrite the formula as a single logarithm.
b) Rewrite the formula in exponential form.
c) Rewrite the formula, solving for P.

Answer 1

log P = 1/2 log k + 1/2 * 3logR
= log(√k) + log√(R^3)
= log√(kR^3)

P = √(kR^3)