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

log P = 1/2 log k + 1/2 * 3logR
= log(√k) + log√(R^3)
= log√(kR^3)
P = √(kR^3)
Respond to this Question
Similar Questions

Astrophysics
I'm having trouble understanding the formulas for determining a planet's distance and mass. A planet's distance is related to the period of revolution and the mass of the central star (e.g, the sun). The relationship is called Kepler's … 
algebra
logarithms Solve the following equations 3^x2=6 Add 2 to both sides of the equation to start. Whatever operation you do to one side of an equation you must do to the other side as well. 3^x  2 + 2 = 6 + 2 3^x = 8 Changing to logs: … 
Physics
A 21.0kg satellite has a circular orbit with a period of 2.37 h and a radius of 8.50×106 m around a planet of unknown mass. If the magnitude of the gravitational acceleration on the surface of the planet is 7.10 m/s2, what is the … 
Math
The period of revolution of a planet around the sun is the time it takes for the planet to complete one orbit of the sun. The period, P years, is give by Kepler's third law P^2=D^3, where D is the average distance from the sun in astronomical … 
Math Help Please
Which of the following expressions is equal to log (x sqrty)/z^5 A. log x + log (1/2) + log y– log 5 – log z B. log [x + (1/2)y – 5z] C. log x + (1/2)log y – 5 log z d. [(1/2) log x log y]/(5 log z) 
math(Please help)
1) use the properties of logarithms to simplify the logarithmic expression. log base 10 (9/300) log  log 300 log 9 = 2 log 3 log 300 = log 3 + log 100 = log 3+2 I just do not know how to put these together now! 
math
Logarithm!!! Select all of the following that are true statements: (a) log(2x) = log(2) + log(x) (b) log(3x) = 3 log(x) (c) log(12y) = 2 log(2) + log(3y) (d) log(5y) = log(20y) – log(4) (e) log(x) = log(5x) – log(5) (f) ln(25) … 
college algebra
Kepler’s third law. According to Kepler’s third law of planetary motion, the ratio t^2/r^3 has the same value for every planet in our solar system. R is the average radius of the orbit of the planet measured in astronomical units … 
physics
According to Kepler's third law, the orbital period T of a planet is related to the radius R of its orbit by T2 R3. A planet's orbit is larger than Earth's by a factor if 3.39. What is the planet's orbital period? 
precalc(LOGS) CONFUSED!
How do I rewrite without logarithms?? 2. log x= log a  4 log b 3. ln t= 3/2 ln a  ln p 4. log y = 3 log x + log 17