43. the surface area of jupiter is 6.14 × 1010 km2, and the surface area of earth is 5.10 × 108 km². without using a calculator but using the table of logarithms, find how many times greater the surface area of jupiter is than the surfacearea of earth.

120.393

Step-by-step explanation:

Jupiter: 6.14x10¹⁰ km²

Earth: 5.10x10⁸ km²

earth.x=jupiter

5.10x10⁸.x = 6.14x10¹⁰

㏒(5.10x10⁸.x) = ㏒(6.14x10¹⁰)

㏒ 5.10 + ㏒ 10⁸ + ㏒ x = ㏒ 6.14 + ㏒ 10¹⁰

㏒ 5.10 + 8 ㏒ 10 + ㏒ x = ㏒ 6.14 + 10 ㏒ 10

According to the logarithm table:

㏒ 5.10 = 0.7075

㏒ 6.14 = 0.7881

㏒ 10 = 1

0.7075 + 8.1 + ㏒ x = 0.7881 + 10.1

0.7075 + 8 + ㏒ x = 0.7881 + 10

8.7075 + ㏒ x = 10.7881

㏒ x = 10.7881 - 8.7075

㏒ x = 2.0806

x = 120.393

So, Jupiter is 120.393 times bigger than Earth.

good luck on your studies! : )

david edward.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4