how many times stronger is a magnitude 7 earthquake than a magnitude 5 earthquake

Question

how many times stronger is a magnitude 7 earthquake than a magnitude 5 earthquake

 

A magnitude of 5 earthquake is 10 times stronger than a magnitude 4 earthquake.

 

A magnitude of 7 earthquake is 10 x 10 x 10 = 1000 times stronger than a magnitude 4 earthquake

 

 

 

please help me with the working out too :)

Answer 1

Each increase of 1 in the earthquake strength scale corresponds to an increase by a factor of 10 in the strength of the earthquake.

 

Let x₅ = strength of a magnitude 5 earthquake

 

The strength of a magnitude 6 earthquake is

 

x₆ = 10x₅

 

For a magnitude 7 earthquake,

 

x₇ = 10x₆ = 10(10x₅) = 100x₅

 

The magnitude 7 earthquake is 100 times as strong as the magnitude 5 earthquake.  The 100 comes from the increase in the scale from 5 to 7, which is an increase of 2, so you multiply the strength of the weaker earthquake by 10^7-5 = 10² = 100, and that gives you the strength of the stronger earthquake.