Answer to Question #268100 in Algebra for John

Question

The magnitude of an earthquake is given by 𝑀 = log 𝐼

where M is the Richter scale value of an earthquake, and I is the intensity of the earthquake. An earthquake of magnitude 6.4 is measured and the following aftershock has a magnitude or 4.1.

Determine algebraically how many times more intense, to the nearest whole, the earthquake is compared to the aftershock.

Answer 1

$$M=\log_{10}I=>I=10^M$$

$$\dfrac{I_E}{I_{after}}=\dfrac{10^{M_E}}{10^{M_{after}}}=10^{M_E-M_{after}}$$

$$=10^{6.4-4.1}=10^{2.3}\approx200$$

An earthquake is 200 times more intense in comparison with the following aftershock.