.
The relation between the number of time in days, D, it takes for a planet to revolve around the Sun
is related to the planet’s average distance from the Sun, k, in millions of kilometres is defined by
logD = 3/2 logk-0.7. How much longer does it take Mars than Venus to orbit the Sun
if Mars is 207 million km and Venus is 108 million km away from the Sun?
equation orientation: https://gyazo.com/61b74df513162501c4701a08f0cbab60
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See how simple the calculations are.
Time for Mars to make one revolution around the Sun
= - 0.7 = use your calculator =
= - 0.7 = use your calculator, again = 2.773955518.
It gives for Mars
= = use your calculator = 594 days (rounded).
Similar calculations for Venus
Time for Venus to make one revolution around the Sun
= - 0.7 = use your calculator =
= - 0.7 = use your calculator, again = 2.350135633
.
It gives for Venus
= = use your calculator = 224 days (rounded).
The problem asks about the difference
- = 594 - 224 = 370 days (approximately). ANSWER
Solved.
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The major goal of this problem is to teach you using your calculator for similar tasks.
First, you make straightforward calculations to find the logarithm values, using given formula.
Next, you potentiate to restore the numbers from the found logarithm values.
In this problem, there is NO ANY NEED to manipulate with formulas for logarithms.
This problem is not intended for such manipulations.